Question

what must the charge (sign and magnitude) of a 2.45 g particle be for it to remain stationary when placed in a downward-directed electric field of magnitude 590 n/c?

Answer 1

For the particle to be stationary, net force vertically must be zero. That means, the weight acting downwards must be equal in magnitude to the electric force acting upwards on the particle. Since electric field is directed downwards and electric force is acting upwards, particle is negatively charged.

Since Fnet = 0,
Weight = Electric Force
mg = qE
(0.00245)(9.81) = q(590)
q = 4.07 x 10^-5

Hence charge is -4.07 x 10^-5