Q: What is the force on a charge $$q$$ moving with velocity $$\vec{v} in a $$magnetic field $$\vec{B}$$?

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

Q: If a proton in a cyclotron has a final speed of $$4.59 \times 10^7$ m/s, what is its kinetic energy? (Proton mass m = 1.67$$ \times $$10^{-27} kg)$$

$$K = \frac{1}{2}mv^2$ = 1.76 \times 10$$^{-12}$$ J

Question 1

A proton with a kinetic energy of $$11 	imes 10^6$ eV enters a region with a uniform magnetic field of 1.2$ T. What is the radius of its circular path? (Proton mass m = 1.67$$ 	imes $$10^{-27} kg$$, charge $$q = 1.60 	imes 10$$^{-19}$$ C)

Accepted Answer

$$0.40 m$$

Question 2

Which equation correctly gives the speed $$v of a $$particle with kinetic energy $$K$$ and mass $$m$$?

Accepted Answer

$$v = \sqrt{2K/m}$$

Question 3

In a mass spectrometer, why do particles with greater mass follow a path with a larger radius?

Accepted Answer

Because $$r = \frac{mv}{|q|B}$$, so increasing $$m$$ increases $$r$$ for constant $$v$$, $$q$$, and $$B.$$

Question 4

A charged particle moves perpendicular to a uniform magnetic field. Which of the following statements is true?

Accepted Answer

The particle moves in a circle at constant speed.

Question 5

What is the force on a charge $$q$$ moving with velocity $$\vec{v} in a $$magnetic field $$\vec{B}$$?

Accepted Answer

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

Question 6

In a velocity selector, what is the condition for a particle to pass through undeflected?

Accepted Answer

$$qE = qvB \implies v = E/B$$

Question 7

A current-carrying wire is placed in a uniform magnetic field. What is the direction of the force on the wire?

Accepted Answer

Perpendicular to both the current and the magnetic field (Right Hand Rule).

Question 8

Which of the following best describes the Hall effect?

Accepted Answer

A voltage develops across a conductor when it carries current in a magnetic field.

Question 9

A cyclotron accelerates particles using which principle?

Accepted Answer

Alternating electric field and constant magnetic field to increase particle energy.

Question 10

If a proton in a cyclotron has a final speed of $$4.59 	imes 10^7$ m/s, what is its kinetic energy? (Proton mass m = 1.67$$ 	imes $$10^{-27} kg)$$

Accepted Answer

$$K = \frac{1}{2}mv^2$ = 1.76 	imes 10$$^{-12}$$ J

Question 11

A particle with charge $$q$$ and mass $$m$$ enters a region with a uniform magnetic field $$B at $$velocity $$v$$ perpendicular to $$B. $$What is the period $$T of $$its circular motion?

Accepted Answer

$$T = \frac{2\pi m}{qB}$$

Question 12

Which of the following is NOT a correct statement about the motion of a charged particle in a uniform magnetic field?

Accepted Answer

The particle's speed changes due to the magnetic force.

Question 13

In a mass spectrometer, what is the purpose of the velocity selector?

Accepted Answer

To ensure only particles with a specific velocity enter the magnetic field region.

Question 14

A wire loop carrying current $$I is $$placed in a uniform magnetic field $$B. $$What is the net force on the loop?

Accepted Answer

Zero, but there may be a net torque.

Question 15

A charged particle enters a region with both electric field $$E$$ and magnetic field $$B$$ perpendicular to each other. If the particle passes through undeflected, what is its velocity?

Accepted Answer

$$v = E/B$$

Question 16

Which of the following best explains why the Earth's surface magnetic field is measured in gauss rather than tesla?

Accepted Answer

Because the Earth's field is much weaker than 1 tesla; 1 tesla = $$10^4$$ gauss.

Question 17

A particle with charge $$q$$ and velocity $$v$$ enters a magnetic field $$B at an $$angle $$	heta to $$the field. What is the magnitude of the magnetic force?

Accepted Answer

$$F = qvB\sin	heta$$

Week 6 Lec. 1 (Week of 1st Exam)

Study Guide - Practice Questions

Study Guide - Flashcards