11.3 Motion of a Charged Particle in a Magnetic Field

Circular and helical paths traced when velocity crosses the field, the radius and period that follow, and why speed itself never changes.

University Physics Volume 2, 11.3 Motion of a Charged Particle in a Magnetic Field

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8 exercises

11.3 Exercise 1

A uniform magnetic field of magnitude 1.5 T is directed horizontally from west to east. (a) What is the magnetic force on a proton at the instant when it is moving vertically downward in the field with a speed of $4 \times 10^{7} \text{m}/\text{s}?$ (b) Compare this force with the weight w of a proton.

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11.3 Exercise 2

At a given instant, an electron and a proton are moving with the same velocity in a constant magnetic field. Compare the magnetic forces on these particles. Compare their accelerations.

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11.3 Exercise 4

An electron passes through a magnetic field without being deflected. What do you conclude about the magnetic field?

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11.3 Exercise 6

How could you determine which pole of an electromagnet is north and which pole is south?

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11.3 Exercise 7

A cosmic-ray electron moves at $7.5 \times 10^{6} \text{m}/\text{s}$ perpendicular to Earth’s magnetic field at an altitude where the field strength is $1.0 \times 10^{−5} \text{T} .$ What is the radius of the circular path the electron follows?

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11.3 Exercise 9

(a) An oxygen-16 ion with a mass of $2.66 \times 10^{−26} \text{kg}$ travels at $5.0 \times 10^{6} \text{m}/\text{s}$ perpendicular to a 1.20-T magnetic field, which makes it move in a circular arc with a 0.231-m radius. What positive charge is on the ion? (b) What is the ratio of this charge to the charge of an electron? (c) Discuss why the ratio found in (b) should be an integer.

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11.3 Exercise 11

(a) At what speed will a proton move in a circular path of the same radius as the electron in the previous exercise? (b) What would the radius of the path be if the proton had the same speed as the electron? (c) What would the radius be if the proton had the same kinetic energy as the electron? (d) The same momentum?

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11.3 Exercise 13

An alpha-particle $\left(\right. m = 6.64 \times 10^{−27} \text{kg},$ $q = 3.2 \times 10^{−19} \text{C} \left.\right)$ travels in a circular path of radius 25 cm in a uniform magnetic field of magnitude 1.5 T. (a) What is the speed of the particle? (b) What is the kinetic energy in electron-volts? (c) Through what potential difference must the particle be accelerated in order to give it this kinetic energy?

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