PHYS208 Unit 2

An inductor is connected in series to a fully charged capacitor. Which of the following statements are true? - The stored electric field energy can be less than the stored magnetic field energy. - As the capacitor is charging, the current is increasing. - The stored electric field energy can be greater than the stored magnetic field energy. - The stored electric field energy can be equal to the stored magnetic field energy. - As the capacitor is discharging, the current is increasing.

- The stored electric field energy can be less than the stored magnetic field energy. - The stored electric field energy can be greater than the stored magnetic field energy. - The stored electric field energy can be equal to the stored magnetic field energy. - As the capacitor is discharging, the current is increasing.

A bar magnet oriented along the y axis can rotate about an axis parallel to the z axis. Its north pole initially points along j. Consider a second case in which the charge is again some distance in the −i direction from the magnet, but now it is moving toward the center of the bar magnet, that is, with its velocity along i. Due to its motion in the magnetic field of the bar magnet, the charge will experience a force in which direction?

-k

An electromagnetic wave is propagating in the positive x direction. At a given moment in time, the magnetic field at the origin points in the positive y direction. In what direction does the electric field at the origin point at that same moment?

-z direction

The inductor has inductance 0.300 H and carries a current in the direction shown that is decreasing at a uniform rate, di/dt = - 1.90×10−2 A/s. Find the self-induced emf.

0.0057 V

The inductor has inductance 0.260 H and carries a current in the direction shown. The current is changing at a constant rate. The potential between points a and b is V(ab) = 1.04 V, with point a at higher potential. If the current at t=0 is 12.0 A, what is the current at t=2.00 s?

4.00 A

Which of the following statements are true concerning the creation of magnetic fields? - A distribution of electric charges at rest creates a magnetic field at all points in the surrounding region. - A permanent magnet creates a magnetic field at all points in the surrounding region. - A moving electric charge creates a magnetic field at all points in the surrounding region. - A single stationary electric charge creates a magnetic field at all points in the surrounding region. - An electric current in a conductor creates a magnetic field at all points in the surrounding region.

A permanent magnet creates a magnetic field at all points in the surrounding region, a moving electric charge creates a magnetic field at all points in the surrounding region, and an electric current in a conductor creates a magnetic field at all points in the surrounding region.

What is true about time-varying electromagnetic fields?

A time-varying magnetic field will produce an electric field and a time-varying electric field will produce a magnetic field.

The magnetic dipole moment (μ) of a coil depends on the current (I), the area of the coil (A), and the number of loops (N). Rank the three different coils of wire in order by the magnitude of their magnetic dipole moment.

ALL EQUAL: Coil 1 = single coil with area 10 cm2 and I=6A. Coil 3 = coil with 6 loops each with an area of 10 cm2 and I=1A. Coil 2 = single coil with area 20cm2 and I=3A.

A resistor is connected across an AC source. What would constitute a graph that shows the instantaneous current through the resistor and the instantaneous voltage across the resistor?

Amplitudes are in the same relationship as the dc circuit -- V = IR; Current is in phase with voltage -- crests and troughs occur together.

A conducting rod is shown moving to the right along U-shaped conducting rails. The apparatus is in a uniform magnetic field perpendicular to the plane of the figure (B = X). As viewed from above, in what direction does the induced current flow in the U-shaped apparatus?

An induced current flows counterclockwise in the U-shaped apparatus.

A resistor, an inductor, and a switch are all connected in series to an ideal battery of constant terminal voltage. Suppose at first the switch is open, and then, at some initial time t = 0, it is closed. Which of the following statements are true? - The steady-state value of the current depends on the inductance of the inductor. - At the instant the switch is closed, the current begins to increase at a rate that depends upon the value of the inductance of the inductor. - The steady-state value of the current depends on the resistance of the resistor. - At the instant the switch is closed, the current reaches its steady-state value.

At the instant the switch is closed, the current begins to increase at a rate that depends upon the value of the inductance of the inductor; the steady-state value of the current depends on the resistance of the resistor.

The magnitude of the magnetic field at a certain distance from a long, straight conductor is represented by B. What is the magnitude of the magnetic field at twice the distance from the conductor?

At twice the distance, the magnitude of the field is B/2.

A circular loop of wire lies flat on a level table top in a region where the magnetic field vector points straight upward. The magnetic field suddenly vanishes. As viewed from above, in what direction does the induced current flow in the loop of wire?

Counterclockwise

T/F: Ampère's law can be used to analytically find the magnetic field at the center of a circle formed by a current-carrying conductor.

False

T/F: Ampère's law can be used to analytically find the magnetic field at the center of a square loop carrying a constant current.

False

The torque (τ) that is exerted on a magnetic dipole moment (μ) depends on the orientation of the magnetic dipole moment. Rank the three loops of wire carrying current in order by the magnitude of the torque exerted on them.

Greatest Torque --> Normal to loop is perpendicular to magnetic field. Normal to loop is at 45 degrees with respect to magnetic field. Normal to loop is parallel to magnetic field. <-- Least Torque

What is true regarding transformers?

In a transformer, if the secondary coil contains more loops than the primary coil, then it is a step-up transformer, and a transformer is used to increase or decrease an alternating current voltage.

Electric rail cars often use magnetic braking. The brake consists of a set of electromagnets that are held just above the rails. To brake the train, the electromagnets are switched on, creating a magnetic field that induces eddy currents in the metal rails passing beneath them. The diagrams represent a view from above, looking down at the rail through the electromagnet. The electromagnet moves to the right, and the magnetic field points into the screen. What correctly represents the eddy currents induced in the rails?

In diagram B eddy currents are flowing clockwise in the area beneath the left end of the electromagnet and counterclockwise in the area beneath the right end of the electromagnet. The magnetic flux increases under the leading edge of the electromagnet and decreases under its trailing edge. Therefore, by Lenz's law, the induced magnetic field will point out of the screen under the leading edge and into it under the trailing edge. The eddy currents in choice B have the right directions to induce such magnetic fields, according to the right-hand rule.

A bar magnet oriented along the y axis can rotate about an axis parallel to the z axis. Its north pole initially points along j. A positive charge (+q) is placed some distance in the −i direction from the magnet. Assume that no charges are induced on the magnet. Assume that the length of the magnet is much smaller than the separation between it and the charge. As a result of magnetic interaction (i.e., ignore pure Coulomb forces) between the charge and the bar magnet, the magnet what torque?

No torque (stationary charge)

A circular loop of conducting wire is moving through a uniform magnetic field. Is a non-zero emf induced in the loop?

No, the emf is zero.

A long, straight, vertical wire carries a current upward. Due east of this wire, in what direction does the magnetic field point?

North

A conducting rod is free to slide on two parallel rails with negligible friction. At the right end of the rails, a voltage source of strength V in series with a resistor of resistance R makes a closed circuit together with the rails and the rod. The rails and the rod are taken to be perfect conductors. The rails extend to infinity on the left. The arrangement is shown in the figure. There is a uniform magnetic field of magnitude B, pervading all space, perpendicular to the plane of rod and rails. The rod is released from rest, and it is observed that it accelerates to the left. In what direction does the magnetic field point?

Out of the plane of the figure

Suppose that an electromagnetic wave is traveling toward the east. At one instant at a given point, the electric field vector points upward. What is the direction of the magnetic field at this same given point and instant in time?

South

The inductor has inductance 0.300 H and carries a current in the direction shown that is decreasing at a uniform rate, di/dt = - 1.90×10−2 A/s. Which end of the inductor, a or b, is at a higher potential?

Terminal a is at a higher potential since the coil pushes current through from b to a and if replaced by a battery it would have the + terminal at a.

A capacitor is connected across an AC source. Suppose the capacitance of the capacitor is reduced by a factor of 2. What happens to the capacitive reactance of the inductor?

The capacitive reactance is doubled

A charged particle enters into a uniform magnetic field such that its velocity vector is perpendicular to the magnetic field vector. Ignoring the particle's weight, what type of path will the particle follow?

The charged particle will follow a circular path.

At a given location in space, the magnetic field in an electromagnetic wave is increasing. How is the electric field changing at that same location?

The electric field is increasing.

Two loops of wire, each having a different radius, encircle an infinitely long solenoid, as shown in (Figure 3). The magnetic field B⃗ is zero outside the solenoid. The current through the solenoid is increasing with time, causing the magnetic field inside the solenoid to increase with time. What is true about the emf around the wire loops?

The emf around the two wire loops is the same and is non-zero.

Consider an electromagnetic wave propagating through a region of empty space. How is the energy density of the wave partitioned between the electric and magnetic fields?

The energy density of an electromagnetic wave is equally divided between the magnetic and electric fields.

The figure (A shown with more waves than B but reaching the same position) shows the electromagnetic field as a function of position for two electromagnetic waves traveling in a vacuum at a given moment. Which statement about the frequency and speed of the waves is correct?

The frequency of wave A is greater than that of wave B, but the speeds of the two waves are the same.

A conducting rod is being dragged along conducting rails. The magnetic field is directed out of the screen. In what direction does the induced current flow through the light bulb?

The induced current flows through the bulb from the right to the left.

Two long parallel wires are placed side by side on a horizontal table. The wires carry equal currents in the same direction. Which of the following statements are true? - The magnetic field is a maximum at a point midway between the two wires. - The magnetic force between the two wires is attractive. - The magnetic field at a point midway between the two wires is zero. - The magnetic force between the two wires is repulsive.

The magnetic force between the two wires is attractive, and the magnetic field at a point midway between the two wires is zero.

What physical property does the symbol I(encl) represent?

The net current through the loop

A conducting rod is free to slide on two parallel rails with negligible friction. At the right end of the rails, a voltage source of strength V in series with a resistor of resistance R makes a closed circuit together with the rails and the rod. The rails and the rod are taken to be perfect conductors. The rails extend to infinity on the left. The arrangement is shown in the figure. Assuming that the rails have no resistance, what is the most accurate qualitative description of the motion of the rod?

The rod will accelerate but the magnitude of the acceleration will decrease with time; the velocity of the rod will approach but never exceed a certain terminal velocity.

A resistor, an inductor, and a switch are all connected in series to an ideal battery of constant terminal voltage. What does the time constant for the circuit represent?

The time constant represents the time required for the current to reach 63% of the maximum current.

A typical MRI magnet may be a solenoid that is 2.0 m long and 1.0 m in diameter, has a self-inductance of 4.4 H, and carries a current of 750 A. A normal wire carrying that much current would dissipate a great deal of electrical power as heat, so most MRI magnets are made with coils of superconducting wire cooled by liquid helium at a temperature just under its boiling point (4.2 K). More of the wire then warms up and loses its superconducting properties, thus dissipating even more energy as heat. Because the latent heat of vaporization of liquid helium is quite low (20.9 kJ/kg), once the wire begins to warm up, all of the liquid helium may boil off rapidly. This event, called a quench, can damage the magnet. If part of the magnet develops resistance and liquid helium boils away, rendering more and more of the magnet nonsuperconducting, how will this quench affect the time for the current to drop to half of its initial value?

The time will be shorter because the resistance will increase.

Two concentric loops of wire are carrying currents in opposite directions. Describe the net force and the torque on either of the current loops.

There is a net force on each loop that causes them to repel each other.

A bar magnet is oriented perpendicular to a uniform magnetic field. Describe the force and/or torque on the magnet.

There is a net torque on the magnet in a counterclockwise direction.

T/F: Ampère's law can be used to analytically find the magnetic field around a straight current-carrying wire.

True

T/F: Ampère's law can be used to analytically find the magnetic field inside a toroid. (A toroid is a doughnut shape wound uniformly with many turns of wire.)

True

Which of the following statements are true for magnetic field lines? - Magnetic field lines are close together in regions of space where the magnitude of the magnetic field is weak, and they are farther apart in regions where it is strong. - Unlike electric field lines, magnetic field lines are continuous. - At every point in space, the magnetic field vector at that point is tangent to the magnetic field line through that point. - Magnetic field lines can never intersect. - Magnetic field lines point in the direction of the magnetic force acting on a charge.

Unlike electric field lines, magnetic field lines are continuous; at every point in space, the magnetic field vector at that point is tangent to the magnetic field line through that point; and magnetic field lines can never intersect.

Rank the wavelength of the electromagnetic waves, in order from longest to shortest

Wavelength: Radio waves < Microwaves < Infrared light < Visible light < UV light < X-rays < Gamma rays

A resistor, an inductor, and a capacitor are connected in series to an AC source. Under what conditions will the impedance of the circuit increase as the inductive reactance increases?

When the inductive reactance is greater than or equal to the capacitive reactance

A bar magnet oriented along the y axis can rotate about an axis parallel to the z axis. Its north pole initially points along j. Now the charge is replaced by an electrically neutral piece of initially unmagnetized soft iron (for example, a nail) that is not moving. As a result of the magnetic interaction between the soft iron and the bar magnet, what will happen to the magnet?

Whichever pole of the magnet is closest to the iron will be attracted to the iron.

Which of the following choices of path allow you to use Ampère's law to analytically find B⃗(r⃗)? a. The path must pass through the point r⃗. b. The path must have enough symmetry so that B⃗(r⃗)⋅dl⃗ is constant along large parts of it. c. The path must be a circle.

a and b: The path must pass through the point r⃗; The path must have enough symmetry so that B⃗(r⃗)⋅dl⃗ is constant along large parts of it.

A wire loop is rotating at a constant angular frequency within a uniform magnetic field B⃗. The orientation of the magnetic field is shown at three moments: a) when area is perpendicular with B field b) when area is 45 degrees with B field c) when area is parallel with B field Rank the orientations from lowest to highest magnitude of the instantaneous induced emf.

a) perpendicular < b) 45 degrees < c) parallel (induced emf is equal to the rate of change of the magnetic flux, which is greatest when the flux is zero)

A conducting rod is shown moving in a uniform magnetic field (B = X, v = ->). Which of the following statements are true? a) An electric field is established in the rod directed from point a to point b. b) The free charges in the rod are acted upon by a magnetic force. c) The magnitude of the potential difference in the rod is proportional to the strength of the magnetic field. d) The magnitude of the potential difference in the rod is inversely proportional to the length L of the rod. e) The magnitude of the potential difference in the rod is proportional to the velocity v of the rod.

a, b, c, e) An electric field is established in the rod directed from point a to point b. The free charges in the rod are acted upon by a magnetic force. The magnitude of the potential difference in the rod is proportional to the strength of the magnetic field. The magnitude of the potential difference in the rod is proportional to the velocity v of the rod.

Which of the following statements are true concerning electromagnetic induction? a) It is possible to induce a current in a closed loop of wire located in a uniform magnetic field by either increasing or decreasing the area enclosed by the loop. b) It is possible to induce a current in a closed loop of wire without the aid of a power supply or battery. c) It is possible to induce a current in a closed loop of wire remaining at rest and located in a uniform magnetic field. d) It is possible to induce a current in a closed loop of wire by changing the orientation of a magnetic field enclosed by the wire. e) It is possible to induce a current in a closed loop of wire by changing the strength of a magnetic field enclosed by the wire.

a, b, d, e) It is possible to induce a current in a closed loop of wire located in a uniform magnetic field by either increasing or decreasing the area enclosed by the loop, in a closed loop of wire without the aid of a power supply or battery, by changing the orientation of a magnetic field enclosed by the wire, and by changing the strength of a magnetic field enclosed by the wire.

A conducting rod is free to slide on two parallel rails with negligible friction. At the right end of the rails, a voltage source of strength V in series with a resistor of resistance R makes a closed circuit together with the rails and the rod. The rails and the rod are taken to be perfect conductors. The rails extend to infinity on the left. The arrangement is shown in the figure. What is the acceleration a_r(t) of the rod? Take m to be the mass of the rod. Express as a function of V, B, the velocity of the rod v_r(t), L, R, and the mass of the rod m.

a_r(t) = [VLB − v_r(t)L^2B^2]/mR To achieve a high acceleration, which is necessary for a useful gun, a magnetic field of large magnitude and a high voltage are advantageous.

The circle on the integral means that B⃗(r⃗) must be integrated...

along any closed path that you choose.

The inductor has inductance 0.260 H and carries a current in the direction shown. The current is changing at a constant rate. The potential between points a and b is V(ab) = 1.04 V, with point a at higher potential. Is the current increasing or decreasing?

decreasing

Ampère's law is often written ∮B⃗(r⃗)⋅dl⃗ = μ(0)I(encl). The integral above is... - the integral throughout the chosen volume. - the surface integral over the open surface. - the surface integral over the closed surface bounded by the loop. - the line integral along the closed loop. - the line integral from start to finish.

the line integral along the closed loop.

A conducting rod is free to slide on two parallel rails with negligible friction. At the right end of the rails, a voltage source of strength V in series with a resistor of resistance R makes a closed circuit together with the rails and the rod. The rails and the rod are taken to be perfect conductors. The rails extend to infinity on the left. The arrangement is shown in the figure. What is the terminal velocity v_t reached by the rod?

v_t = V/LB A larger magnetic field increases the acceleration of the rod, but lowers the terminal velocity.