Peoples Physics Book Version-2

http://www.ck12.org Chapter 15. Magnetism Version 2

Example 1: Find the Magnetic Field

Question: An electron is moving to the east at a speed of 1. 8 × 106 m/s. It feels a force in the upward direction
with a magnitude of 2.2? 10−^12 N. What is the magnitude and direction of the magnetic field this electron just passed
through?

Answer: There are two parts to this question, the magnitude of the electric field and the direction. We will first focus
on the magnitude.

To find the magnitude we will use the equation

FB=qvBsinθ

We were given the force of the magnetic field( 2 .2? 10−^12 N)and the velocity that the electron is traveling( 1. 8 ×
106 m/s). We also know the charge of the electron( 1. 6 × 10 −^19 C). Also, because the electron’s velocity is
perpendicular to the field, we do not have to deal with sinθbecause sinθof 90 degrees is 1. Therefore all we
have to do is solve for B and plug in the known values to get the answer.

FB=qvBsinθ

Solving for B:

B=

FB

qvsinθ

Now, plugging the known values we have

B=

FB

qvsinθ

=

2 .2? 10−^12 N

1. 6 × 10 −^19 C× 1. 8 × 106 m/s× 1

= 7 .6T

Now we will find the direction of the field. We know the direction of the velocity (east) and the direction of the force
due to the magnetic field (up, out of the page). Therefore we can use the second right hand rule (we will use the left
hand, since an electron’s charge is negative). Point the pointer finger to the right to represent the velocity and the
thumb up to represent the force. This forces the middle finger, which represents the direction of the magnetic field,
to point south. Alternatively, we could recognize that this situation is illustrated for apositiveparticle in the right
half of the drawing above; for a negative particle to experience the same force, the field has to point in the opposite
direction: south.

Example 2: Circular Motion in Magnetic Fields

Consider the following problem: a positively charged particle with an initial velocity of~v 1 , chargeqand massm
traveling in the plane of this page enters a region with a constant magnetic field~Bpointing into the page. We are
interested in finding the trajectory of this particle.