ep2 prelecture assignments
A charge of +0.001 CC is 1 mm to your right and another charge of +1000 CC is 1 mm to your left. You are holding a charge of −1 CC. Which of the following statements is/are true?
- The force on the charge you are holding from the charge on your left is 1,000,000 times as large as the force from the charge on your right. - The magnitude of the force on the charge you are holding would be the same if it were +1 CC instead of −1 CC.
The magnetic force on a charged particle in a magnetic field is zero if
- the charged particle is at rest - the charged particle moves parallel to the magnetic field
A cylindrical Gaussian surface surrounds an infinite line of charge. The flux Φe through the two flat ends of the cylinder is
0
The current through a wire is measured as the potential difference ΔΔ V is varied. What is the wire's resistance?
0.02 Ω (R is the inverse of the slope of I versus ΔV.)
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 shown in order by the magnitude of the torque exerted on them.
1. Normal to loop is perpendicular to magnetic field (greatest torque) 2. Normal to loop is at 45 degrees with respect to magnetic field. 3. Normal to loop is parallel to magnetic field (least torque) *The torque depends on the sine of the angle between the magnetic field and the normal to the loop. The sine of that angle is a maximum when the two are perpendicular
A uniform magnetic field points upward, parallel to the page, and has a magnitude of 7.85 mT. A negatively charged particle (q = -3.32 µC, m = 2.05 pg) moves through this field with a speed of 67.3 km/s at a 42° with respect to the magnetic field, parallel to the page as shown. What is the magnitude of the magnetic force on this particle?
1.17 mN FB=qvBsin θ FB=(3.32⋅10^−6 C)(67.3⋅10^3 m/s)(7.85⋅10^−3 T)sin(42∘)=1.17⋅10^−3 N
Wire 2 is twice the length and twice the diameter of wire 1. What is the ratio R2/R1 of their resistances?
1/2
If the top circuit has an oscillation frequency of 1000 Hz, the frequency of the bottom circuit is
1410 Hz The circuit frequency is ω=(√1/LC), and two similar capacitors hooked in series have a combined capacitance of C/2
If you can build a cyclotron with twice the radius and with the magnetic field twice as strong, by what factor would the allowed maximum particle energy increase?
16
How many laws are named after Kirchhoff?
2 (Kirchhoff's loop law and Kirchhoff's junction law)
Two long straight wires are parallel to each other and are separated by 78 mm. The current in wire 1 is 3.55 A and the current in wire 2 is 2.75 A. What is the force per unit length between the two wires?
2.5 × 10-5 N/m F/L=(μ0*I1*I2)/(2πr) F/L=((4π×10−7 T⋅m/A)(3.55 A)(2.75 A)) / 2π(0.078 m) = 2.5×10^−5 N/m
The potential difference across the 10 resistor is
20 V *I=V/(R1+R2) I=30/(10+5) = 2 A --> V=IR V=(2A)*(10) = 20V
Every minute, 120 C of charge flow through this cross section of the wire. The wire's current is
2A (I = Q/Δt)
A circular coil of conducting wire, with a radius of 4.48 cm and 25 turns, is in a 1.67-T magnetic field. When the coil's dipole moment vector makes an angle of 34° with the magnetic field, a 0.537-N•m torque is exerted on the coil. What is the current in the coil?
3.65 A τ=μB sinθ τ=μB sinθ, τ=NIAB sinθ The current in this coil is I=τ/(NAB sinθ) = (.537 N•m)/((25)π(0.0448 m^2)(1.67 T) s(in34º)) = 3.65 A
If you can build a cyclotron with twice the radius, by what factor would the allowed maximum particle energy increase? Assume that the magnetic field remains the same.
4
The electric flux through the shaded surface is
400 N m^2/C.
A 144-Ω light bulb is connected to a conducting wire that is wrapped into the shape of a square with side length of 83.0 cm. This square loop is rotated within a uniform magnetic field of 454 mT. What is the change in magnetic flux through the loop when it rotates from a position where its area vector makes an angle of 30° with the field to a position where the area vector is parallel to the field?
41.9 mWb ΔΦB=BA(cos θf−cos θi) = (0.454 T)(0.83 m)^2(cos 0∘−cos 30∘) = 0.0419 Wb = 41.9 mWb
A 144-Ω light bulb is connected to a conducting wire that is wrapped into the shape of a square with side length of 83.0 cm. This square loop is rotated within a uniform magnetic field of 454 mT. The loop rotates from a position where its area vector makes an angle of 30° with the field to a position where the area vector is parallel to the field in 56.3 ms. What is the induced current through the light bulb?
5.17 mA I=(ΔΦB/Δt)/R = (((0.454 T)(0.83 m)^2(cos 0∘−cos 30∘))/0.0563s)/144 Ω = .00517 A = 5.17 mA
A uniform magnetic field points upward, parallel to the page, and has a magnitude of 7.85 mT. A negatively charged particle (q = -3.32 µC, m = 2.05 pg) moves through this field with a speed of 67.3 km/s perpendicular to the magnetic field, as shown. The magnetic force on this particle is a centripetal force and causes the particle to move in a circular path. What is the radius of the particle's circular path?
5.29 mm FB=qvB=mv^2/r r=(mv)/(qB)=((2.05×10^−15 kg)(67.3×10^3 m/s))/((3.32×10^−6 C)(7.85×10^−3 T))=0.00529 m
A 144-Ω light bulb is connected to a conducting wire that is wrapped into the shape of a square with side length of 83.0 cm. This square loop is rotated with a frequency of 60 Hz within a uniform magnetic field of 454 mT. This means the loop makes half a revolution in 8.33 ms. What is the induced current in the light bulb when the loop rotates from a position where its area vector is opposite the magnetic field to a position where its area vector is parallel to the magnetic field?
521 mA I=(ΔΦB/Δt)/R = (((0.454 T)(0.83 m)^2(cos 0∘−cos 180∘))/0.00833s)/144 Ω = .521 A = 521 mA
A 65-cm segment of conducting wire carries a current of 0.35 A. The wire is placed in a uniform magnetic field that has a magnitude of 1.24 T. What is the angle between the wire segment and the magnetic field if the force on the wire is 0.26 N?
67º F=ILB sinθ θ=sin^−1(F/(ILB)) = sin^−1(0.26 N/(0.35 A)(0.65 m)(1.24 T)) = 67∘
A positive and a negative charge are released from rest in vacuum. They move toward each other. As they do,
A negative potential energy becomes more negative. (The charges have opposite signs, so U is negative. And U increases in magnitude as r decreases.)
What device provides a practical way to produce a uniform electric field?
A parallel-plate capacitor
If the bar magnet is flipped over and the south pole is brought near the hanging ball, the ball will be
Attracted to the magnet (steel is not a permanent magnet member, and its magnetic moments will align based on the external magnetic field. If North Pole is brought near then the magnetic moments will align in a way to have south pole and it will get attracted, and same with the South Pole)
The charge of sphere 2 is twice that of sphere 1. Which vector below shows the force of 2 on 1?
B
Which is the direction of the net force on the charge at the lower left?
B
The magnetic field is decreasing. What is the induced electric field?
B (he electric field is in the same direction that induced current would flow if there were a loop in the field)
The magnetic field of a point charge is given by
Biot-Savart's law
Who discovered electromagnetic induction?
Both Faraday and Henry
Two protons, A and B, are next to an infinite plane of positive charge. Proton B is twice as far from the plane as proton A. Which proton has the larger acceleration? Neglect interactions between the protons.
Both have the same acceleration.
The figure shows a wire that is connected to a power supply and suspended between the poles of a magnet. When the switch is closed, the wire deflects in the direction shown. Which of the dashed boxes A-D represents the position of the north magnetic pole?
C (Deflection is predicted by the relation F = qv x B)
Which capacitor discharges more quickly after the switch is closed?
Capacitor A (smaller tau discharges faster --> The time constant of the circuit is Τ = RC, and 2×6 is smaller than 3×5)
Two positive charges are equal. Which has more electric potential energy?
Charge A (Electric potential energy increases toward the positive plate.)
For charged particles, what is the quantity q/m called?
Charge-to-mass ratio
What is the SI unit of charge?
Coulomb
What quantity is represented by the symbol J?
Current density
What is the direction of the electric field at the dot?
D
Which of the following would double the amount of current flowing through a piece of metal wire?
Double the voltage across it (According to Ohm's law, the current is proportional to the voltage when the resistance stays the same.)
Currents circulate in a piece of metal that is pulled through a magnetic field. What are these currents called?
Eddy currents
A rod attracts a positively charged hanging ball. The rod is
Either negative or neutral.
What is the amount of electric field passing through a surface called?
Electric flux
If the resistivity of copper is less than that of gold at room temperature, which of the following statements must be true?
Electrons in gold are more likely to be scattered than electrons in copper at room temperature when they are accelerated by the same electric field (Resistivity is a property of the material independent of its shape (dimensions). It is more and more difficult for electrons to travel through the material with a higher resistivity.)
What is the electron drift speed in a typical current-carrying wire?
Extremely slow (≈10^−4 m/s)
What is the shape of the trajectory that a charged particle follows in a uniform magnetic field?
Helix
What property of a real battery makes its potential difference slightly different than that of an ideal battery?
Internal resistance
A uniform magnetic field points upward, parallel to the page, and has a magnitude of 7.85 mT. A negatively charged particle (q = -3.32 µC, m = 2.05 pg) moves through this field with a speed of 67.3 km/s at a 42° with respect to the magnetic field, parallel to the page as shown. What is the direction of the magnetic force on this particle?
Into the page (right hand rule. One way to do this is to point your fingers in the direction of the velocity and curl your fingers in the direction of the magnetic field. Your thumb will indicate the direction of the force on a positive charge. In this problem, a positive charge would experience a force out of the page so the negative charge experiences a force into the page)
An induced current flows clockwise as the metal bar is pushed to the right. The magnetic field points
Into the screen.
At the negative terminal of the battery the electron has electric potential energy. What happens to this energy as the electron jumps from the negative to the positive terminal?
It is converted to kinetic energy.
A proton is released from rest at the dot. Afterward, the proton
Moves downward with an increasing speed.
The equation I = ΔV/R is called
Ohm's law
A long, straight wire extends into and out of the screen. The current in the wire is
Out of the screen (right-hand rule)
The direction of the magnetic force on the proton is
Out of the screen (right-hand rule)
What is the electric potential energy of an electron at the negative end of the cable, relative to the positive end of the cable? In other words, assume that the electric potential of the positive terminal is 0 V and that of the negative terminal is −12V. Recall that e=1.60E-19C
PE=(V1−V2)*e PE=(−12V−0V)(−1.6E−19C) PE = 1.92E-18 J *also the same as the amount of Work done
Two protons, A and B, are in an electric field. Which proton has the larger acceleration? Neglect interactions between the protons.
Proton A (The field is stronger where the field lines are closer together and weaker where the field lines are farther apart.)
If released from rest, the current loop will
Rotate counterclockwise (There is a net torque, but no net force)
Which spherical Gaussian surface has the larger electric flux?
Surface B (Flux depends only on the enclosed charge, not the radius.)
Gauss's law is useful for calculating electric fields that are
Symmetric
What is the SI unit for the strength of the magnetic field?
Tesla
Which has a larger resistance, a 60 W lightbulb or a 100 W lightbulb?
The 60 W bulb (The power is P = (ΔV)^2/R, where ΔV = 120 V for both)
Assume that two of the electrons at the negative terminal have attached themselves to a nearby neutral atom. There is now a negative ion with a charge −2e at this terminal. What are the electric potential and electric potential energy of the negative ion relative to the electron?
The electric potential is the same and the electric potential energy is twice as much.
While unhooking the jumper cables, the positive and negative cables almost touch and a spark jumps between the ends of the cables. This spark is caused by the movement of electrons through the air between the battery terminals. In what direction are the electrons traveling during the spark?
The electrons are traveling from the negative to the positive terminal (The positive terminal is at a higher potential than the negative terminal. Unless provided with energy, positive charges will flow from a high to a low potential, and negatively charged electrons will flow from a low to a high potential.)
Two loops of wire, each having a different radius, encircle an infinitely long solenoid. The magnetic field B 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. Which statement is true?
The emf around the two wire loops is the same and is non-zero (The magnetic flux through either wire loop is simply BA, where A is the area of the solenoid. Thus the rate of change of magnetic flux through each wire loop is the same, resulting in the same emf)
Four +2 μC charges are placed at the positions (10 cm, 0 cm), (−10 cm, 0 cm), (0 cm, 10 cm), and (0 cm, −10 cm) such that they form a diamond shape centered on the origin. A charge of +5 μC is placed at the origin. If the force between a +2 μC and a +5 μC charge separated by 10 cm has a magnitude of 9 N, which of the following can we say about the force on the +5 μC charge at the origin in this case?
The force on the charge at the origin is 0.
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 (Using the right-hand rule for the magnetic force, we find that the right side of the rod becomes positively charged, causing the current to flow from the right side to the left side of the bulb)
How do the resistances of two conducting wires compare if they have the same length, but one is twice the radius of the other?
The thicker wire has one-fourth the resistance of the thinner wire (A thicker wire will allow more current to flow with the same voltage difference driving it, because the resistance is inversely proportional to the area of the wire.)
The bar magnet is pushed toward the center of a wire loop. Which is true?
There is a clockwise induced current in the loop if one looks down from the point above of the loop.
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 (The loops create magnetic fields in opposite directions, similar to what happens when two bar magnets are arranged with their north poles close to 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 (In a uniform field, the magnet experiences a net torque that tends to align the north pole in the direction of the 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.
They are all equal (The magnetic dipole moment (μ) is proportional to the area of the loop (A), the current (I), and the number of coils (N). So, all three cases have the same magnetic dipole moment)
Metals are good conductors of electric current for which of the following reasons?
They possess high concentrations of free electrons.
In an RC circuit, what quantity is represented by the symbol τ?
Time constant
What are the units of potential difference?
Volts
You are given three pieces of wire that have different shapes (dimensions). You connect each piece of wire separately to a battery. The first piece has a length L and cross-sectional area A. The second is twice as long as the first, but has the same thickness. The third is the same length as the first, but has twice the cross-sectional area. Rank the wires in order of which carries the most current (has the lowest resistance) when connected to batteries with the same voltage difference.
Wire of length L and area 2A (most current) Wire of length L and area A Wire of length 2L and area A (least current) *A thicker wire will have a lower resistance and allow more current to flow with the same voltage across it. A shorter wire will also have a lower resistance and allow more current to flow with the same voltage across it.
Which of the following are ohmic materials?
Wires and resistors
The magnetic field of a straight, current-carrying wire is
around the wire
Consider three plastic balls (A, B, and C), each carrying a uniformly distributed charge equal to either +Q, -Q or zero, and an uncharged copper ball (D). A positive test charge (T) experiences the forces shown in the figure when brought very near to the individual balls. The test charge T is strongly attracted to A, strongly repelled from B, weakly attracted to C, and strongly attracted to D. What is the nature of the force between balls A and B?
attractive
Consider three plastic balls (A, B, and C), each carrying a uniformly distributed charge equal to either +Q, -Q or zero, and an uncharged copper ball (D). A positive test charge (T) experiences the forces shown in the figure when brought very near to the individual balls. The test charge T is strongly attracted to A, strongly repelled from B, weakly attracted to C, and strongly attracted to D. What is the nature of the force between balls A and D?
attractive
Consider three plastic balls (A, B, and C), each carrying a uniformly distributed charge equal to either +Q, -Q or zero, and an uncharged copper ball (D). A positive test charge (T) experiences the forces shown in the figure when brought very near to the individual balls. The test charge T is strongly attracted to A, strongly repelled from B, weakly attracted to C, and strongly attracted to D. What is the nature of the force between balls A and C?
attractive in smaller magnitude than balls A and B
In a capacitor, the peak current and peak voltage are related by the
capacitive reactance
The junction rule describes the conservation of which quantity? Note that this rule applies only to circuits that are in a steady state.
charge
The magnetic field of a solenoid is analogous to the electric field of a
charged parallel-plate capacitor
Gauss's law applies to
closed surfaces.
All other things being equal, current will be larger in a wire that has a larger value of
conductivity
You are presented with several long cylinders made of different materials. Which of them are likely to be good conductors of electric current?
copper, aluminum, gold
how can you demagnetize a magnet (such as one that usually hangs on a fridge?)
heat it
The electric potential inside a capacitor
increases linearly from the negative to the positive plate.
This is a current phasor. The magnitude of the instantaneous value of the current is
increasing
The equivalent resistance for a group of parallel resistors is
less than any resistor in the group.
The figure shows the path of a charged particle moving in a magnetic field directed into the screen. What is the particle's charge?
negative (A negative charge gives the correct direction for the centripetal force F = qv x B)
Consider three plastic balls (A, B, and C), each carrying a uniformly distributed charge equal to either +Q, -Q or zero, and an uncharged copper ball (D). A positive test charge (T) experiences the forces shown in the figure when brought very near to the individual balls. The test charge T is strongly attracted to A, strongly repelled from B, weakly attracted to C, and strongly attracted to D. What is the nature of the force between balls C and D?
neither attractive nor repulsive
A circular loop of conducting wire is moving through a uniform magnetic field. Is a non-zero emf induced in the loop?
no (Since the magnetic flux through the loop is constant in time, the rate of change of the flux is zero; thus there is no induced emf)
There is a 12 V potential difference between the positive and negative ends of the jumper cables, which are a short distance apart. An electron at the negative end ready to jump to the positive end has a certain amount of potential energy. On what quantities does this electrical potential energy depend?
only the potential difference and the charge
The analysis of AC circuits uses a rotating vector called a
phasor
You are presented with several wires made of the same conducting material. The radius and drift speed are given for each wire in terms of some unknown units r and v. Rank the wires in order of decreasing electron current.
radius = 2r, drift speed = 2.5v (most current) radius = 3r, drift speed = 1v radius = 4r, drift speed = 0.5v radius = 1r, drift speed = 5v (least current)
The specific magnetic behavior of ferromagnetic materials is due to
the domain structure
The drift speed of the electrons in a wire depends strongly on which of the following factors?
the electric field in the wire
If a negatively charged rod is held near a neutral metal ball, the ball is attracted to the rod. This happens because
the rod polarizes the metal.
You are holding a positive charge and there are positive charges of equal magnitude 1 mm to your north and 1 mm to your east. What is the direction of the force on the charge you are holding?
to the southwest
The electric field inside a conductor in electrostatic equilibrium is
zero
If three uncharged styrofoam balls are placed together and agitated so that one gains +3 C of charge and another gains +4 C of charge, how much charge must there be on the third one?
−7 CC
