Q: A magnetic dipole moment $$\vec{m} in a $$uniform magnetic field $$\vec{B}$$ experiences a torque given by:

$$\vec{\tau} = \vec{m} \times \vec{B}$$

Question 1

A copper wire and a nichrome wire are both cylindrical and have the same length and cross-sectional area. The conductivity of copper is $$6.0 	imes 10^7$\ \$$Omega^{-1}$$\,\mathrm{m}^{-1}$$, and that of nichrome is $$6.7 	imes 10^5$\ \$$Omega^{-1}$$\,\mathrm{m}^{-1}. $$Which of the following best explains why copper has a higher conductivity than nichrome?

Accepted Answer

The electrons' mean time between collisions in copper is higher than that in nichrome.

Question 2

Which of the following statements about superconductors is correct?

Accepted Answer

Superconductors have zero resistance below a certain critical temperature.

Question 3

According to Ohm's Law, the current $$I$$ through a resistor is given by $$I = \frac{\Delta V}{R}. If $$the potential difference across an ohmic wire is halved, what happens to the current?

Accepted Answer

The current is halved.

Question 4

A long piece of ohmic wire is connected to an 8 V battery and the current is measured to be 0.30 A. If the same wire is connected to a 4 V battery, what current would you expect?

Accepted Answer

$$0.15\ \mathrm{A}$$

Question 5

For a given potential difference across a length of wire, which of the following changes will increase the current by a factor of 4? (Assume each change is made independently.)

Accepted Answer

Increase the radius of the cross-section of the wire by a factor of 2.

Question 6

Which of the following best describes the magnetic field lines around a bar magnet?

Accepted Answer

They emerge from the north pole and enter the south pole outside the magnet.

Question 7

A vertical wire carries current upward through the center of a horizontal table. A compass rests on the table. In which direction does the north pole of the compass point?

Accepted Answer

Tangential to the circle, in the direction given by the right-hand rule (counterclockwise when viewed from above).

Question 8

The magnitude of the magnetic field at a distance $$r$$ from a long straight wire carrying current $$I is $$given by:

Accepted Answer

$$B = \frac{\mu_0$ I}{2\pi r}$$

Question 9

A solenoid has 3000 windings, a length of $$0.35\ \mathrm{m}$$, and the magnetic field inside is $$0.27\ \mathrm{T}. $$What is the current in the windings? ($$\mu_0$ = 1.26 	imes 10$$^{-6}$$\ \mathrm{T}\cdot\mathrm{m}/\mathrm{A})$$

Accepted Answer

$$25\ \mathrm{A}$$

Question 10

A charged particle moves with velocity $$\vec{v}$$ perpendicular to a uniform magnetic field $$\vec{B}. $$What is the radius of the circular path it follows?

Accepted Answer

$$r = \frac{mv}{|q|B}$$

Question 11

Which of the following changes will decrease the radius of the circular path of an electron in a magnetic field? Select all that apply.

Accepted Answer

Decrease the potential difference in the electron gun.

Question 12

A current-carrying wire is placed in a uniform magnetic field. The force on a segment of the wire of length $$L$$ carrying current $$I at an $$angle $$	heta to $$the field $$B is $$given by:

Accepted Answer

$$F = I L B \sin 	heta$$

Question 13

Two long, parallel wires carry equal currents in opposite directions. What is the direction of the force between the wires?

Accepted Answer

The wires repel each other.

Question 14

A current loop in a uniform magnetic field experiences a torque. The magnitude of the torque is given by:

Accepted Answer

$$	au = N I A B \sin 	heta$$

Question 15

Ampère's Law states that the line integral of the magnetic field $$\vec{B}$$ around a closed curve is equal to:

Accepted Answer

$$\mu_0$ I_{	ext{through}}$$

Question 16

A magnetic dipole moment $$\vec{m} in a $$uniform magnetic field $$\vec{B}$$ experiences a torque given by:

Accepted Answer

$$\vec{	au} = \vec{m} 	imes \vec{B}$$

Question 17

Which of the following best describes the direction of the magnetic field at the center of a circular loop carrying current $$I$$?

Accepted Answer

Perpendicular to the plane of the loop, direction given by the right-hand rule.

Question 18

A particle with positive charge is at the origin and moving in the positive $$y$$ direction. At which of the following points is the magnetic field due to the particle zero?

Accepted Answer

At a point on the $$y-$$axis (directly in front of the particle's motion).

Conductivity, Resistance, and Magnetic Fields: Study Notes ch 29

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