Phys 42 Electricity and Magnetism Final Exam Question Set

An AC source that outputsV[t] = (120 V) sin ((30pi rad/s)t)is connected to a 0.500 H inductor.What is the rms voltage across the inductor?

Lecture Notes Week 15 Slide 79

An AC source that outputsV[t] = (120 V) sin ((30p rad/s)t)is connected to a 0.500 H inductor.What is the inductive reactance of the circuit?

Lecture Notes Week 15 Slide 81

An AC source that outputsV[t] = (120 V) sin ((30p rad/s)t)is connected to a 0.500 H inductor. What is the rms current in the circuit?

Lecture Notes Week 15 Slide 83

A typical American home uses an average of 1 kW of power. If this power is brought into the house at 240 V (rms), what rms current is required?

Lecture Notes Week 16 Slide 49

At your job at a chemical company, your boss has asked you to determine the geometry of a stable equilibrium involving a chlorine ion and a carbon dioxide ion, both with charge -e. The carbon dioxide ion is composed of 2 oxygen ions each with an effective charge -2e and a carbon ion with an effective charge +3e. These ions are arranged in a line with the carbon ion halfway between the two oxygen ions. The distance between each oxygen ion and the carbon ion is 3.0 x 10-11 m. Assuming that the chlorine ion is on a line that is perpendicular to the axis of the carbon dioxide ion and that this line goes through the carbon ion, what is the angle between this line and a line between the chlorine ion and one of the oxygen atoms? For simplicity, you assume that the carbon dioxide ion does not deform in the presence of the chlorine ion.

Lecture Notes Week 1 Slide 26

You have a job at a company that designs air purifier systems. Your team is designing a machine that can filter dangerous carbon monoxide (CO) molecules out of the air using electric fields. Your task is to calculate the net force and torque on a CO molecule in a uniform electric field with magnitude 1.1 x 10E6 N/C when the axis of the CO molecule is 30° off from the direction of the field. You are to calculate the torque with respect to the center of mass of the CO molecule. You know that CO molecules are composed of a carbon atom with a mass of 1.99 x 10E-26 kg and an oxygen atom with a mass of 2.66 x 10-26 kg separated by a distance of 1.43 x 10E-10 m. Due to the uneven distribution of electrons, the carbon atom has an effective charge of -0.178e and the oxygen atom has an effective charge of 0.178e.

Lecture Notes Week 1 Slide 58

You are continually having trouble aiming an electron beam in your lab and wonder if it is due to magnetic fields from the power lines running in your building. A blueprint of the building shows that there are two nearby power lines as shown. One is a very long straight line and the other is a loop. Your electron beam apparatus is located at point P. Calculate the magnetic field at P as a function of the currents I1 and I2 and the distances a, b, and c. Segments BC and AD are arcs of concentric circles. Segments AB and DC are straight-line segments. (Diagram on flip side)

Lecture Notes Week 10 Slide 22

While studying for a physics test you are listening to your stereo. Your thoughts drift to stories you have heard about the dangers of household magnetic fields on the body. Examining your stereo wires, you find that most of them are coaxial cable, a thin conducting wire at the center surrounded by insulator, which is in turn surrounded by a conducting shell. The inner wire and the conducting shell are both part of the circuit, carrying the same current through them in opposite directions. To practice for your physics final, you decide to calculate the magnetic field in the insulator and outside the coaxial cable as a function of the current (I0) and the distance from the center of the cable (r). As an additional challenge, you calculate the magnetic field inside the outer conducting shell of the coaxial cable, assuming that the inner radius of the conducting shell is b and the outer radius is c.

Lecture Notes Week 10 Slide 57

Your team is testing the feasibility of a magnetic system to safely move large loads from the back of a truck down to the ground. The system consists of a horizontal metal bar (on which the load is placed) that is connected to two vertical metal rails. The two rails are also connected together electrically at the ground. When the bar slides down through a horizontal uniform magnetic field, it moves with a controlled constant velocity, even when friction is negligible. Before setting up the laboratory model, your task is to calculate the constant velocity with which the bar slides down the rails as a function of the mass of the bar, the strength of the magnetic field, the length of the bar (which is the same as the distance between the rails), and the resistance of the circuit including the bar and rails.

Lecture Notes Week 12 Slide 29

In a particular region, the magnetic field points up, but its magnitude is non-constant, varying as B(r) = Ar, where r is the horizontal distance away from the center of the field. A horizontal circular loop of radius R has its center at the center of the field. What is the magnetic flux through the loop?

Lecture Notes Week 13 Slide 15

A wire bent at a 90° angle carries a current I. Find the magnetic field at the point P. The wire is very long compared to the distance between the wire and P. (Diagram on flip side)

Lecture Notes Week 13 Slide 17

You are working with a team to bring electricity to remote areas. One simple idea that has been proposed is to run two long parallel wires between the power station and the remote area to create a circuit. However, you are worried about the self-inductance of such a design. You decide to calculate it for a given length l of the two wires, assuming that the wires are separated by a distance D (center-to-center) and have a radius R. To get a rough estimate, you decide to ignore effects associated with the ends of the wires near the power station and remote area (since the wires are very long) as well as magnetic flux inside the wires (since R << D and l).

Lecture Notes Week 14 Slide 13

While evaluating a printed circuit board design, you notice that someone has placed a very long straight trace (essentially a wire) that potentially carries a large current near a rectangular loop. Since the circuit board is for a high speed application where the current may have to change very quickly, you calculate the mutual inductance between the two conductors to see if it will be a problem. (Diagram on flip side)

Lecture Notes Week 14 Slide 20

A 1000 μF capacitor is connected to an AC power supply that produces a rms voltage of 20 V with a frequency of 100 Hz. What is the maximum charge that appears on either capacitor plate?

Lecture Notes Week 15 Slide 71

An AC source that outputsV[t] = (120 V) sin ((30p rad/s)t)is connected to a 0.500 H inductor. What is the frequency of the source?

Lecture Notes Week 15 Slide 77

You are helping to design a power supply for a large electromagnet. Your task is to evaluate the safety of the circuit when the magnet is turned off (by opening a switch). You know that induction can generate a large voltage across the switch when it is opened. You will model the opening of the switch as simultaneously removing the power supply and inserting a large resistance in series in the circuit (the air gap of the switch) as shown in the diagram (moving the switch from a to b). You decide to calculate the potential across R2 just after the switch is opened, after being closed for a long time. For purposes of getting a numerical estimate, you assume that R2 = 100 R1. (Circuit Diagram on flip side)

Lecture Notes Week 16 Slide 72

You have a summer internship with an astrophysics group developing a spacecraft that depends only on the sun's radiation pressure for propulsion. Such a craft would have to be relatively lightweight and have a very large and reflective "sail." To be feasible, the radiation pressure on the sail must at least balance the sun's attractive force on the craft. To get you familiar with the problem, your advisor asks you to consider a spacecraft with a 5 kg body and a sail made from the latest carbon fiber material with an areal density of 1 g/m2. How large would the sail have to be so that the sun's radiation pressure just balances out the sun's attractive gravitational force on the spacecraft? The sun radiates power at a rate of 3.9 x 10E26 Watts and has a mass of 1.99 x 10E30 kg.

Lecture Notes Week 17 Slide 46

You have a summer job in a research laboratory with a group investigating the possibility of producing power from fusion. The device being designed confines a hot gas of positively charged ions, called plasma, in a small sphere with a radius of 2.0 cm. The charge density of the plasma in the sphere is r[r] = r0 (r/R)where r0 =6.0x10E-5 C/m^3 and R=2.0cm. Positively charged Tritium ions are to be injected into the plasma toward the center of the sphere. Your job is to determine the speed that a Tritium ion should have when it enters the plasma sphere so that its velocity is zero when it reaches the center. Tritium is an isotope of Hydrogen with one proton and two neutrons with a mass of 5.0 x 10E-27 kg. As a first step, you calculate the electric field inside the sphere.

Lecture Notes Week 2 Slide 43

You are helping to design an electron microscope to investigate the structure of the HIV virus. A new device to position the electron beam consists of a charged circle. This circle is divided into two half circles separated by a thin insulator so that one half of the circle can be charged positively and the other half can be charged negatively. The electron beam will go through the center of the circle. To complete the design, your job is to calculate the electric field at the center of the circle as a function of the amount of positive charge on the half circle, the amount of negative charge on the half circle, and the radius of the circle.

Lecture Notes Week 2 Slide 9

Your job is to evaluate an electron gun designed to initiate an electron beam. Free electrons with a very small velocity are first produced by being boiled off a heating element. This heating element is a spherical electrode 0.10 mm in diameter that has a constant charge of -5.0 pC. Next, the electrons travel 1.0 cm to pass through the center of a 5.0 mm diameter hole in the middle of a 3.0 cm diameter charged circular disk. The electrons travel perpendicular to the plane of the disk and the disk's charge density is kept at 0.30 μC/m^2. These electrons then travel another 20 cm through a very good vacuum to the end of the gun. For most applications, the electrons must reach the end of the gun with a speed of at least 10E7 m/s. Your first step is to determine if the electrons will be going fast enough in the current design. Your boss has pointed out that the hole in the disk is too large to ignore in your calculations. Using your physics text you find that the electron mass is 9.11 x 10E-31 kg.

Lecture Notes Week 5 Slide 15

The parallel plate capacitor model has two circular plates, each with a diameter of 15 cm. The distance between the plates can be varied between 0 and 20 cm. What is the range of capacitance it can have?

Lecture Notes Week 5 Slide 68

What is the capacitance of the Earth?

Lecture Notes Week 5 Slide 74

The first telegraphic messages crossed the Atlantic Ocean in 1858, by a cable 3000 km long laid between Newfoundland and Ireland. The conductor in this cable consisted of seven copper wires, each of diameter 0.73 mm, bundled together and surrounded by an insulating sheath. Calculate the resistance of the cable. Use 3 x 10E-8 Ω•m for the resistivity of copper, which was much less pure (and thus much more resistive) than the copper available today.

Lecture Notes Week 6 Slide 75

You are helping to design a circuit that will control electromechanical relays at a natural gas burning power plant. The switch is first connected at point 'a,' charging the capacitor. When it reaches 90% of its maximum voltage, the circuit trips a relay and the switch flips its connection from point 'a' to 'b.' The capacitor then discharges. Your job is to determine a value for the resistors R1 and R2 so that it takes 1.5 s for the capacitor to reach 90% of its max voltage. Other teams have fixed the values of the other components to be V = 9 V and C = 8 μF. (Circuit Diagram on flip side)

Lecture Notes Week 7 Slide 65

You are working with a research group investigating radioactive isotopes that might be useful in fighting cancer. You are working on a way to transport alpha particles (He nuclei) from where they are made to another room where they will collide with other material to form the radioactive isotopes. Since the isotopes do not live very long, it is important to know precisely how much time it takes to transport the alpha particles. Your job is to design the part of the transport system that will use a magnetic field to deflect the beam of alpha particles (m = 6.64 x 10-27 kg, q = 3.2 x 10E-19 C) through an angle of 90°. The beam will be traveling horizontally in an evacuated tube. At the place the tube is to make a 90° turn, you decide to put a dipole magnet which provides a uniform vertical magnetic field of 0.030 T. Your design has a tube of the appropriate shape between the poles of the magnet. However, before you submit your design for consideration, you must determine how long it will take the alpha particles in the uniform magnetic field to make the 90°-turn.

Lecture Notes Week 8 Slide 28

The hospital in which you work treats certain cancers using a beam of doubly ionized alpha particles (He2+ with a mass of m). These alpha particles are initially traveling with a speed v. You are in charge of deflecting this beam so it hits a patient's cancerous region. The deflection is accomplished by running the beam through a uniform electric field generated between two parallel, flat, metal plates (called electrodes). The beam is perpendicular to the electric field when it enters that region, which has a length L in the initial direction of the beam. To treat the tumor in today's patient, you need to deflect the incoming beam so that it travels at an angle q relative to its original direction. How strong must the electric field be in order to produce this deflection? Express your answer in terms of (only) the given quantities and known constants.

Midterm 1 Question 1

You have landed a summer job working with an Astrophysics group investigating the origin of high- energy particles in the galaxy. The group has just discovered a large spherical nebula with a radius R. The nebula has a positive charge density that varies with distance from its center r[r] = r0(R/r). At the center of this sphere of charge is a very small neutron star. The group had detected electrons (with mass m) emerging from the nebula. A friend of yours thinks that the electrons are coming from the neutron star. To test that theory, she asks you to calculate the minimum speed that an electron would need to start from the neutron star to just barely make it outside the nebula. Express your answer in terms of (only) the given quantities and known constants. In addition, check the units of your answer explicitly so the grader can see that they are correct.

Midterm 1 Question 2

Your neighbor's child wants to build a display demonstrating the electrostatic force for a science project. Her idea is to have a small ball of mass m with a positive charge q suspended from a light string of length D. This ball would be held at an angle q away from the vertical by an electric field generated by a horizontal positively charged rod with a length L. This rod, with a uniform charge density, would be held at the same vertical height as the ball. The end of the rod nearest to the ball would be a distance W away from the ball. What charge would the rod need to make this display possible? Express your answer in terms of (only) the given quantities and known constants.

Midterm 1 Question 3

Your job is to evaluate a device designed to produce a beam of electrons. After being produced at a heated electrode, the electrons (with mass m and charge -e) are given an initial velocity vi as they pass through the center of a thin ring with a diameter d. The electrons' velocity is perpendicular to the plane of the ring. The charge on the ring is negative, uniformly distributed, and has a magnitude Q. Your task is to find the speed of the electrons when they exit the gun, a distance L away from the disk. The inside of the gun is kept at a very good vacuum. First find a purely symbolic answer in terms of the given quantities. Then, find a numerical answer using the following values, vi =2.0m/s, d=3cm,Q=3x10E-10 C,L=40cm, m=9.11x10E-31 kg.

Midterm 2 Question 1

While trying to find the power ratings of your appliances you find their circuit diagrams. Looking them over, your friend believes there must be a typo in the circuit diagram of your toaster. The heating element that toasts the bread is listed as having a resistance of 5 ohms. A variable resistor (RV), which is changed by a knob on front of the toaster, can take on values between 2 and 20 ohms. Your friend feels that with these values, the heater could not toast bread properly. Based on the circuit diagram, given below, you decide to calculate the maximum power output by the heating element. (Circuit Diagram on flip side)

Midterm 2 Question 2

You have a part-time job as an assistant technician for a cable TV company. During a recent earthquake, a 1.0 mile long underground cable line was crushed at some point. This line is made up of two parallel copper wires of the same diameter and same length, which are normally kept insulated from each other. However, at the place where the line is crushed, the two wires make contact. Your need to find this place so that the wire can be dug up and fixed. You isolate the line from the rest of the network by disconnecting both wires of the line at both ends of its 1.0 mile length. You then go to one end of the line and connect the ends of the two wires to the two terminals of a 6.0-V battery. An ammeter shows that under these conditions, 1 A of current flows through your circuit. You then disconnect everything and travel to the other end of the line, where you repeat the process and find that a current of 1/3 A flows through the circuit. Where will you advise your company to dig to find the crushed part of the line? (Be as specific as possible.)

Midterm 2 Question 3

You are part of a NASA team exploring ways to protect astronauts on a space station from high energy charged particles. One idea is to surround the outside of the station with a uniform magnetic field of strength B. In order to prepare for any case, you have been asked to figure out how far from the walls of the station the magnetic field should extend (w) in order to prevent particles with a mass m, charge q, and kinetic energy E from hitting the space station walls. You also need to specify in which direction the magnetic field should point. To get started, you decide to make the calculation for the case in which the high energy charged particles have velocities that are initially perpendicular to the side of the space station. Express your answer in terms of B, m, q, E, and known constants. Verify explicitly and show that your answer has the correct units. (Diagram on flip side)

Midterm 3 Question 1

You decide to try to get free electricity by placing a coil of wire on the ground below a very long, straight, high-voltage power line that is 9 meters above the ground. The power line has a maximum potential of 200 kV and carries a maximum current of 10,000 A. Both the current and the voltage vary sinusoidally at 60 Hz (the current has the form I = Imaxsin(2pft) where f = 60 s-1, with an equivalent equation for the potential). You will make the coil by wrapping wire around the legs of a large table, giving you a rectangular coil with sides that are 1 meter and 2 meters long. Because you want to use the coil to power the appliances in your house, you need to figure out how many loops of wire you will need in your coil to generate an emf with a peak value of 170 Volts. You also need to figure out how the coil should be oriented with respect to the power line for maximum efficiency. As part of your solution, draw a clear picture that shows how the coil will be oriented with respect to the overhead power line, in addition to calculating the necessary number of loops of wire.

Midterm 3 Question 2

While repairing a solenoid magnet in your research lab, you notice that a large, current carrying wire runs near the solenoid. You wonder whether the magnetic field of that wire could significantly alter the magnetic field inside the solenoid. The figure shows the solenoid (circle) and wire viewed from one end of the solenoid. The solenoid has a diameter of 4 cm and is much longer than it is wide. The wire that makes up the solenoid is wound at 3000 turns per meter and carries a current of 500 A in the clockwise direction when in normal operation. The external wire that you are worried about is located outside the solenoid at the middle of its length and is in a plane that is perpendicular to the axis of the solenoid. This wire is composed of three sections. The curved section is one-sixth of a circle with a radius of curvature of 5 cm. The center of curvature is the same as the center of the solenoid. The two straight parts are directed radially (as shown by the dashed lines) and are 6 cm long. You decide to calculate (1) whether the current in the wire makes the field inside the solenoid larger or smaller and (2) the current that would have to flow in the external wire in order for it to alter the magnetic field at the center of the solenoid by 1%. (Diagram on flip side)

Midterm 3 Question 3

Two protons with mass mp, both moving with equal speeds v are initially very far apart, but on a head-on collision course. What is closest distance that they get towards each other?

Practice Final Exam Question 1

You are working on a team evaluating a new type of silicon solar cell. Instead of having a rectangular geometry, the new design looks like a very long, narrow cylinder with a radius of 1.35 μm. At radii less than 0.9 μm, the silicon has a uniform charge density of +0.0015 C/cm^3. Between 3 radii of 0.9 μm and 1.35 μm, the silicon has a uniform charge density of -0.0012 C/cm^3. Your task is to find the potential difference between the outside edge and the central axis of the cylinder, which will give the voltage of the solar cell.

Practice Final Exam Question 2

Your work team is investigating the possibility of making electrically controlled valves for an internal combustion engine. Your assignment is to determine the stability of the valve by calculating the force on each of its four sides. The valve is a thin but strong rectangular piece of non-magnetic material, 0.35 cm x 1.83 cm, that has a loop of current carrying wire along its edges. The valve is attached to the engine by a hinge along one of its long sides. The valve is located within a region with a uniform magnetic field of 0.15 T such that the field lies in the plane of the valve and is parallel to the short sides of the rectangle. To operate the valve, a 1.7 A current enters one of the short sides of the valve and leaves via the opposite short side as shown in the diagram. To give different currents through the wires along the long sides of the valve, a resistor is part of the wire on each of these sides. The value of the resistor on one side is twice that on the other side. (Diagram on flip side)

Practice Final Exam Question 3

You are working in a group that is trying to create nuclear fusion using high-powered pulsed lasers. To generate the pulse, the lasers need a lot of energy very quickly. One proposal is to power the lasers using the energy stored in a inductor. As shown in the figure, the inductor will be shaped like a toroid with a square cross section with side length a and the inner radius of the toroid will be b. The toroid will have N turns of wire. Your group leader is concerned that the self-inductance of the toroid will prevent it from transferring its energy to the laser quickly enough and so asks you to calculate that self-inductance. (Diagram on flip side)

Practice Final Exam Question 4

At your new job at a startup company designing power supplies, you have been assigned to develop an AC power supply (e = e0cos wt) that will run both a resistive load and an inductive load at the same time (see the circuit diagram). Because you have to make sure that the power supply can output enough current, you decide to begin by calculating the maximum current the voltage source must deliver in terms of e0, R, L, and w. (W = omega)(Diagram on flip side)

Practice Final Exam Question 5

You and a friend are doing laundry when you unload the dryer and the discussion turns to static electricity. Your friend wants to get some idea of the amount of charge that causes static cling. You immediately take two empty soda cans (each with mass m) from the recycling bin. You tie the cans to the two ends of a string (one to each end) and hang the center of the string over a nail sticking out of the wall. Each can now hangs straight down a distance L from the nail, with the two cans touching each other. You then take your flannel shirt from the dryer and run it over the cans, which move apart until they each hang stationary at an angle of q from the vertical. Assuming that there are equal amounts of charge on each can, you now calculate the amount of charge transferred from your shirt. Express your answer in terms of (only) the given quantities and known constants. Be sure to state any assumptions explicitly. After you have found your symbolic answer, use the following values to calculate a numerical answer: m = 120 g, L = 75 cm, q = 4°.

Practice Midterm 1 Question 1

You are working with the Public Health department to design an electrostatic trap for pollution particles. A typical particle (mass m) enters the device and is exposed to ultraviolet radiation that knocks off electrons, giving it a positive charge q. At this time, this typical particle is located a distance D1 from a very long negatively charged wire with a linear charge density of -l and is moving toward the wire in a direction perpendicular to the wire at a speed of v0. A detector for the particle is located a distance D2 (D2 < D1) from the wire. In order to design the proper kind of detector, your colleagues need to know the speed that a typical emission particle will have when it hits the detector. Express your answer in terms of (only) the given quantities and known constants.

Practice Midterm 1 Question 2

You are part of a team assigned to design a tiny electronic oscillator for a nanomachine. You start by trying to understand a simple model consisting of an electron moving along an axis that runs through the center of and is perpendicular to the plane of a flat ring with an inner radius Ri and an outer radius Ro. The ring will carry an overall positive charge Q. You decide to first calculate how the acceleration of the electron depends on the displacement (x) of the electron from the center of the ring along the axis perpendicular to the ring. Remember that acceleration is a vector quantity. Express your answer in terms of (only) the given quantities and known constants.

Practice Midterm 1 Question 3

You are helping to design a semiconductor ion implantation machine. In this apparatus, a "gun" shoots doubly ionized He ions (He2+ with mass m) at a small semiconductor sample that is mounted in such a way that it remains neutral. To minimize damage to the semiconductor, the He ions, which leave the gun traveling vi, must be going slower than vf when they hit the sample. To slow the ions, a wire of length L with a uniformly distributed positive charge Q is placed on the opposite side of the sample from the gun, with the sample located along the axis of the wire. Your task is to decide how far away from one end of the wire the sample must be placed. You decide to approximate the gun as being very far away from the sample. First find a purely symbolic answer in terms of the given quantities. Then, find a numerical answer using the following values, m=6.7x10E-27 kg, vi =4x10E5 m/s, vf =100m/s,L=10cm,Q=10nC.

Practice Midterm 2 Question 1

As a member of the safety group for the space shuttle scientific program, you have been asked to evaluate an electronics design change. In order to improve the reliability of a circuit to be used in the next shuttle flight, the experimental design team has suggested adding a second 12 V battery to the circuit. The equivalent resistances of the proposed design are shown below. You are worried about the heat generated by the device with the 20 W resistance because it will be located next to a sensitive low temperature experiment, so you do the appropriate calculation. (Circuit Diagram on flip side)

Practice Midterm 2 Question 2

You have a summer job in the University ecology lab. Your supervisor asks you to duplicate an electromagnet that she has borrowed. She tells you that this electromagnet is made by wrapping a wire many times around a piece of iron and provides you with all the necessary parts, including the same type of wire and an identical iron core. To complete your task, you need to know how much wire to wrap around the iron. Unfortunately, you cannot simply unwrap the wire from the borrowed magnet because that would destroy it. On the side of the borrowed electromagnet, it states that when a potential difference of 12 V is put across the ends of its wire, there is a current of 0.06 A through the wire. With a brilliant flash of insight, you realize that since the cross-sectional area and the conductivity is the same for both the magnet's wire and the wire you have, you can find the length with a simple experiment. You cut off a 100-foot piece of wire from your supply, attach it to a 1.5-V flashlight battery and measure a current of 0.10 A through that wire. Eureka! You can now find the length of the wire in the electromagnet.

Practice Midterm 2 Question 3

Your team is developing a system to safely lower large loads down ramps. One idea involves a load- carrying bar that slides on two parallel conducting rails that run down the sides of the ramp. The bar, which is conducting, is perpendicular to the rails and makes electrical contact with them. At the bottom of the ramp, the two rails are connected together electrically. The bar slides down the rails through a uniform vertical magnetic field, which is supposed to cause the bar to slide down the ramp at a controlled constant velocity even when friction between the bar and the rails is negligible. Your task is to calculate the constant velocity of the bar sliding down the rails as a function of the mass of the load and bar, the strength of the magnetic field, the angle the ramp makes with the horizontal, the length of the bar (which is the same as the distance between the rails), and the resistance of the circuit that includes the bar and rails. As part of your solution, check the units of your answer explicitly and show that they make sense.

Practice Midterm 3 Question 1

While searching through a pile of salvaged electronics, you find an old color TV, that worked using a Cathode Ray Tube (CRT). You remember from your physics class that in a CRT, electrons are accelerated through a high potential difference (20,000 V, according to markings on the label) before traveling through a good vacuum towards the TV screen, which in this case is 40 cm away. On the screen is a grid of dots about 1/100 of an inch apart. When the electron beam hits the dots, a chemical in the dots gives off colored light to produce a picture. Out of curiosity, you decide to determine whether the manufacturer needed to shield the CRT from the Earth's magnetic field, remembering that this field is about 5 x 10E-5 T in magnitude. Since the Earth's magnetic field points in different directions depending on where you are, you decide to make the calculation for the worst case, when the magnetic field is oriented so that it creates the greatest deflection of the electron beam.

Practice Midterm 3 Question 2

You are checking the design parameters of a double solenoid used in a magnetic resonance imaging apparatus. In the apparatus, two very long, tightly wound solenoids are nested concentrically one inside the other. The inner solenoid has radius R1 and n1 turns per unit length. The outer solenoid has radius R2 and n2 turns per unit length. Each solenoid carries the same current I in opposite directions. Your boss has asked you to find the magnitude and direction of the magnetic field both inside the inner solenoid and between the two solenoids in terms of I, n1, n2, R1, and R2. (Draw a picture to show the direction of the fields.)

Practice Midterm 3 Question 3