Question

What is the work done by the magnetic field on the moving charge?
A. No work is done by the magnetic field on the charge.
B. Work done will be maximum.
C. Work done will be minimum.
D. Both (A) and (B).

Answer 1

Hint: Magnetic field is the space around the magnet where the effect of magnet can be felt by another magnet or iron piece. Magnetic fields can also be produced by a moving charge whose intensity can be determined by the velocity and magnitude of charge. The S.I unit of magnetic field is Tesla (T) whereas the C.G.S unit is Gauss (G).

Formula used: $F = q(\vec v\times \vec B)$

Complete step by step answer:
Since the moving charge produces a magnetic field, hence if an external magnetic field is applied, the moving charge will interact with the field and hence it experiences a force or magnetic force. This force is given by $F = q(\vec v\times \vec B)$.
Here, q is the magnitude of charge, ‘v’ is the velocity and ‘B’ is the external applied magnetic field in the region.
Now, this relation of force suggests that the direction of force is perpendicular to the velocity of charge as $\vec v\times \vec B$ is a cross product means the resultant will be perpendicular to both velocity and magnetic field. Thus force is perpendicular to velocity.
Now, as direction of velocity is same as the change in displacement ‘ds’, thus while writing the work done by force:
$W = \int \vec F.\vec {ds}$
Or $W = \int Fds cos\theta$
So, the angle between ‘F’ and ‘ds’ is $90^\circ$ as they are perpendicular. Hence we can say that the work done is zero.
i.e. $W=0$

So, the correct answer is “Option A”.

Note: Students are advised to remember this important result that magnetic fields don’t work on charge. We can directly apply this concept in the motion of charges in a magnetic field. And since the work done is zero, thus the change in kinetic energy is also zero. Hence in a magnetic field, the kinetic energy of the charge remains constant.