Q: A moving charge $$q$$ with velocity $$\vec{v}$$ produces a magnetic field at a point $$P a $$distance $$r$$ away. Which equation gives the magnitude of the magnetic field?

$$B = \frac{\mu_0$}{4\pi} \frac{qv \sin\theta}{r^2$}$$

Question 1

A proton with velocity $$\vec{v}$$ enters a region with a uniform magnetic field $$\vec{B}$$ perpendicular to its velocity. What is the magnitude of the force acting on the proton?

Accepted Answer

$$F = qvB$$

Question 2

A charged particle moves through a velocity selector, which uses perpendicular electric and magnetic fields. If the electric field is $$E$$ and the magnetic field is $$B$$, what velocity $$v$$ must the particle have to pass through undeflected?

Accepted Answer

$$v = \frac{E}{B}$$

Question 3

A wire of length $$L$$ carrying current $$I is $$placed in a uniform magnetic field $$B$$ perpendicular to the wire. What is the magnitude of the force on the wire?

Accepted Answer

$$F = ILB$$

Question 4

A rectangular current loop of area $$A$$ and current $$I is $$placed in a uniform magnetic field $$B. $$What is the maximum torque experienced by the loop?

Accepted Answer

$$	au_{max} = IAB$$

Question 5

A moving charge $$q$$ with velocity $$\vec{v}$$ produces a magnetic field at a point $$P a $$distance $$r$$ away. Which equation gives the magnitude of the magnetic field?

Accepted Answer

$$B = \frac{\mu_0$}{4\pi} \frac{qv \sin	heta}{r^2$}$$

Question 6

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

Accepted Answer

The wires repel each other.

Question 7

What is the magnetic field at the center of a circular loop of radius $$R$$ carrying current $$I$$?

Accepted Answer

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

Question 8

Ampere’s law states that the line integral of the magnetic field around a closed loop is equal to:

Accepted Answer

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

Question 9

A solenoid of length $$l$$ and $$N$$ turns carries current $$I. $$What is the magnetic field inside the solenoid?

Accepted Answer

$$B = \mu_0$ n I$$

Question 10

According to Faraday’s law, the induced emf in a loop is:

Accepted Answer

$$\mathcal{E} = -\frac{d\Phi_B}{dt}$$

Question 11

A metal rod of length $$L$$ moves with velocity $$v$$ perpendicular to a magnetic field $$B. $$What is the motional emf generated across the rod?

Accepted Answer

$$\mathcal{E} = BLv$$

Question 12

A loop is placed in a region where the magnetic field increases with time. According to Lenz’s law, what is the direction of the induced current?

Accepted Answer

It opposes the increase in magnetic flux.

Question 13

A mass spectrometer uses a magnetic field $$B to $$separate ions of mass $$m$$ and charge $$q. If $$the ions enter with velocity $$v$$, what is the radius $$r of $$their circular path?

Accepted Answer

$$r = \frac{mv}{qB}$$

Question 14

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

Accepted Answer

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

Question 15

A rectangular loop of wire is pulled out of a region with a uniform magnetic field at constant velocity. What happens to the induced emf as the loop leaves the field?

Accepted Answer

The emf decreases as the loop leaves the field.

Question 16

A current-carrying wire is placed parallel to another wire. If both carry current in the same direction, what is the force between them?

Accepted Answer

The wires attract each other.

Question 17

A loop of wire with area $$A is $$placed in a magnetic field $$B at an $$angle $$	heta. $$What is the magnetic flux through the loop?

Accepted Answer

$$\Phi_B = BA \cos	heta$$

Question 18

A transformer operates on the principle of electromagnetic induction. Which law explains the induced emf in the secondary coil?

Accepted Answer

Faraday’s law

Question 19

A patient undergoes an MRI scan, which uses a strong magnetic field. If a proton in the patient’s body moves perpendicular to the field, what is the direction of the force on the proton?

Accepted Answer

Perpendicular to both the velocity and the magnetic field

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