Question

A charged particle moves through a magnetic field. In which situation is the magnetic force zero?

a. When the particle moves in the direction of the magnetic field vector.
b. When the particle moves perpendicular to a magnetic field line.
c. When the particle moves perpendicular to the magnetic field vector.

Answer 1

The answer is the option a.

Step-by-step explanation:

We know that magnetic force (Fm) is defined as

Fm = q (v x B)

Where q is a the value of the charge, v is the velocity of the charge and B is the value of the magnetic field.

"v x B" is defined as the cross product between the vectors velocity and magnetic field, and if the angle between them is thetha < 180°, then, the cross product is

v x B = vBsin (thetha)

So,

Fm = qvBsin (thetha)

And, in case in which v and B are parallel vectors, thetha is zero, and,

sin (thetha)=sin (0) = 0

So, Fm=0