Question

The force on a charged particle due to electric and magnetic fields is given by F=qE+ qv x B. Suppose E is along the X-axis and B along the Y-axis. In what direction and with what minimum speed v should a positively charged particle be sent so that the net force on it is zero?

Answer 1

Answer:

For better understanding see the figure.

Given=> F= qE+ q(v x B) = 0

E = -(v x B)

We can say that the direction of v x B should be opposite to the direction of E.

Hence, v should be in positive yz plane.

Now,

E = vB sinФ          

v = E / (B sinФ)

So, for v to be minimum, Ф = 90°

v(min) = F/B

We can conclude that the particle must be projected at a minimum speed of E/B along positive z-axis in which Ф=90°, so that force is zero.