Q: A moving charge generates a magnetic field. Which equation describes the magnetic field at a point due to a charge q moving with velocity $$\vec{v}$$?

$$\vec{B} = \frac{\mu_0$ q \vec{v} \times \hat{r}}{4 \pi r^2$}$$

Question 1

A solenoid at CERN is used to generate a uniform magnetic field for experiments. If the solenoid has n turns per unit length and carries a current I, what is the expression for the magnetic field inside the solenoid?

Accepted Answer

$$B = \mu_0$ n I$$

Question 2

Which of the following best explains why the Earth's magnetic field is much stronger than the Moon's?

Accepted Answer

The Earth spins much faster and has a molten, conducting interior, generating stronger internal currents.

Question 3

A moving charge generates a magnetic field. Which equation describes the magnetic field at a point due to a charge q moving with velocity $$\vec{v}$$?

Accepted Answer

$$\vec{B} = \frac{\mu_0$ q \vec{v} 	imes \hat{r}}{4 \pi r^2$}$$

Question 4

What is the direction of the magnetic field produced by a current-carrying wire, according to the right-hand rule?

Accepted Answer

The magnetic field lines form circles around the wire, with the direction given by curling the fingers of your right hand around the wire when your thumb points in the direction of the current.

Question 5

Two long, parallel wires are separated by a distance r and carry currents I and $$I' in $$the same direction. What is the force per unit length between them?

Accepted Answer

$$\frac{F}{L} = \frac{\mu_0$ I I'}{2 \pi r}$$

Question 6

A straight, current-carrying conductor of infinite length produces a magnetic field at a distance r from the wire. What is the expression for the magnetic field?

Accepted Answer

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

Question 7

Why do computer cables and audio-video cables produce little or no magnetic field?

Accepted Answer

The wires inside the cables carry current in both directions, causing their magnetic fields to cancel each other.

Question 8

A circular current loop of radius a carries a current I. What is the magnetic field at the center of the loop?

Accepted Answer

$$B = \frac{\mu_0$ I}{2a}$$

Question 9

Ampere’s law relates the magnetic field around a closed path to the current enclosed by that path. Which equation represents Ampere’s law?

Accepted Answer

$$\oint \vec{B} \cdot d\vec{l} = \mu_0$ I_{encl}$$

Question 10

Inside a long cylindrical conductor of radius R carrying a uniformly distributed current I, what is the expression for the magnetic field at a distance r from the center (where $$r \u003c R$$)?

Accepted Answer

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

Question 11

What is the SI definition of the ampere based on the force between two parallel conductors?

Accepted Answer

One ampere is the current that causes each of two parallel conductors one meter apart to experience a force of $$2 	imes 10$$^{-7}$$ newtons per meter.

Question 12

A patient undergoing an MRI scan is exposed to a strong magnetic field. Why are the coils bathed in liquid helium?

Accepted Answer

To keep the coils from overheating due to the high currents required.

Question 13

The Bohr magneton is a fundamental unit of magnetic dipole moment. Which equation gives its value?

Accepted Answer

$$\mu_B = \frac{e h}{4 \pi m}$$

Question 14

Which property distinguishes ferromagnetic materials from paramagnetic and diamagnetic materials?

Accepted Answer

Ferromagnetic materials have atomic magnetic moments that line up parallel in domains, leading to strong magnetization.

Question 15

A current-carrying wire is bent into a circle of radius a. What is the direction of the magnetic field at the center of the loop?

Accepted Answer

It is perpendicular to the plane of the loop, determined by the right-hand rule.

Question 16

If a wire carries current into the plane of the page, what is the direction of the magnetic field lines around the wire?

Accepted Answer

Clockwise, as seen from above the wire.

Question 17

A paramagnetic material is placed in an external magnetic field. What happens to the magnetic field inside the material?

Accepted Answer

The magnetic field inside is greater by a factor $$K_m$$ than it would be in vacuum.

Question 18

A wire of length 2a carries a current I. What is the magnetic field at a point a distance x from the wire on its perpendicular bisector?

Accepted Answer

$$B = \frac{\mu_0$ I}{4 \pi x} \frac{2a}{\sqrt{x^2$ + a^2$}}$$

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