Question

1. A small charged bead has a mass of 0.5 g. It is held in a uniform electric field E = 200,000 N/C, up. When the bead is released, it accelerates upward with an acceleration of 20 m/s². What is the charge on the bead

Answer 1

Mass on the bead m= 0.5 g = 0.0005 Kg            (given)

This mass is held in a Uniform Electric Field with Magnitude E=200000 N/C    in upward direction.

When the bead is released, it accelerates in the upward direction with acceleration a = 20 m/s².

We know the force experienced by a charge in Electric field is given by

                                                                F_E = q*E                (upward in the direction of electric field)

Also, the force due to gravity would be

                                                                F_G = m*g              (downward)

Where g is the acceleration due to gravity.

Thus, the net force would be given as

                                                                F = m*a = F_E – F_G = q*E – m*g

Thus,                                                     q =[ m*( a + g ) ] / E

                                   =>         q =[ 0.0005*(20+9.8) ] / (200000)

   =>       q = 7.45 * 10^-8 C

This is the Charge on the bead.