Question

An electron with charge -e and mass m travels at a speed v in a plane

perpendicular to a magnetic field of magnitude B. The electron follows a

circular path of radius R. In a time, t, the electron travels halfway around the

circle. What is the amount of work done by the magnetic field?​

Answer 1

ANSWER

If the velocity

v

of the charged particle has a component parallel to the magnetic field

B

, instead of a circle, the resulting trajectory will be a helical path, as shown in figure. Because the velocity of the particle has a non-zero component along the direction of magnetic field

B

Answer 2

Answer:

The amount of work done by the magnetic field is zero.

Explanation:

The figure formed by an electron with charge -e and mass m travelling at a speed v in a plane perpendicular to a magnetic field of magnitude B is added below.

Fc is the centripetal force provided by the magnetic field.

We know that work done is given by

$W = f.s cosθ$

Here, θ=90°

cos90=0

∴W=0

Therefore,  the amount of work done by the magnetic field is zero.