Q: The Lorentz force law describes the force on a charged particle in electric and magnetic fields. Which equation represents this law?

$$\vec{F} = q\vec{E} + q\vec{v} \times \vec{B}$$

Question 1

A solenoid at CERN generates a uniform magnetic field inside its core. Which equation best describes the magnetic field inside a long solenoid with $$n$$ turns per unit length carrying current $$I$$?

Accepted Answer

$$B = \mu_0$ n I$$

Question 2

A moving charge generates a magnetic field. Which of the following correctly expresses the magnitude of the magnetic field produced by a charge $$q$$ moving with velocity $$v at a $$distance $$r$$ from the charge?

Accepted Answer

$$B = \frac{\mu_0$ |q| v \sin \phi}{4\pi r^2$}$$

Question 3

Two parallel wires are 5.00 cm apart and carry currents in opposite directions. What is the direction of the force between the wires?

Accepted Answer

The wires repel each other

Question 4

Which law is analogous to Gauss’s law for calculating magnetic fields and involves integrating the magnetic field around a closed loop?

Accepted Answer

Ampere’s law

Question 5

A straight, infinitely long conductor carries a current $$I. $$What is the magnitude of the magnetic field at a distance $$r$$ from the wire?

Accepted Answer

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

Question 6

The Lorentz force law describes the force on a charged particle in electric and magnetic fields. Which equation represents this law?

Accepted Answer

$$\vec{F} = q\vec{E} + q\vec{v} 	imes \vec{B}$$

Question 7

A toroidal solenoid with $$N$$ windings carries a current $$I. $$Using Ampere’s law, what is the magnetic field at a radius $$r$$ inside the toroid?

Accepted Answer

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

Question 8

If two very long parallel wires carry equal currents in the same direction, what is the nature of the force between them?

Accepted Answer

The wires attract each other

Question 9

A thick wire of radius $$a$$ carries a uniform current density $$J. $$What is the magnetic field at a distance $$r \u003c a$$ from the center of the wire?

Accepted Answer

$$B(r) = \frac{1}{2} \mu_0$ J r$$

Question 10

What is the fundamental unit of magnetic dipole moment for an electron, known as the Bohr magneton?

Accepted Answer

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

Question 11

A paramagnetic material is placed in an external magnetic field. How does the magnetic field inside the material compare to that in a vacuum?

Accepted Answer

It is greater by a factor $$K_m$$

Question 12

Which of the following best describes ferromagnetism?

Accepted Answer

Atomic magnetic moments line up parallel in domains, and domains align with an external field

Question 13

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

Accepted Answer

Perpendicular to the plane of the loop

Question 14

The right-hand rule for a current-carrying wire states that if you point your thumb in the direction of the current, your fingers curl in the direction of:

Accepted Answer

The magnetic field lines

Question 15

A proton and an electron move perpendicular to each other at the same speed. At the instant shown, what is the direction of the magnetic field produced by the electron at the location of the proton?

Accepted Answer

Into the page

Question 16

The magnetic susceptibility $$\chi_m of a $$material is defined as:

Accepted Answer

$$\chi_m = K_m - 1$$

Question 17

A wire carries a current $$I. At $$what distance from the wire does the magnetic field have a magnitude $$B$$?

Accepted Answer

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

Question 18

Which of the following is true for the net force between two moving charges if their velocity equals the speed of light ($$v = c$$)?

Accepted Answer

The net force is zero

Question 19

In a solenoid, the magnetic field outside the central region is:

Accepted Answer

Approximately zero

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