Question

A proton moving at 4.50 106 m/s through a magnetic field of magnitude 1.80 T experiences a magnetic force of magnitude 7.80 10-13 N. What is the angle between the proton's velocity and the field? (Enter both possible answers from smallest to largest.)
a. in °
b. in °

Answer 1

Concepts and reason

The required concepts to solve the problem are magnetic field, magnetic force and velocity of a charged particle in a magnetic field.

First, using the relation between magnetic field, magnetic force, charge of the particle, velocity of the particle and the angle between the velocity and the field, find the smallest angle between the velocity and the field. Then, using the relation between magnetic field, magnetic force, the charge of the particle, the velocity of the particle and the angle between the velocity and the field, find the largest angle between the velocity and the field.

Fundamentals

When a charged particle enters a magnetic field at an angle, it experiences a magnetic force. The relation between magnetic field, magnetic force, the charge of the particle, the velocity of the particle and the angle between the velocity and the field is,

Here, is the charge of the particle, is the magnetic force, is the magnetic field, is the velocity andis the angle between the velocity and the field.

(a)

The equation for magnetic force is,

Substitute for , for , forandforto find.

The smallest angle between the velocity and the field is,

(b)

The equation for magnetic force is,

Substitute for, for, forandforto find.

The largest angle between the velocity and the field is,

Ans: Part a

Thus, the smallest angle between the velocity and the field is.

Part b

Thus, the largest angle between the velocity and the field is.