Question

Two identical conducting small spheres are placed with their centers 0.270 m apart. One is given a charge of -12.0 nC and the other a charge of -18.0 nC. (a) Find the electric force exerted by one sphere on the other magnitude direction away from the other sphere (b) The spheres are connected by a conducting wire. Find the electric force each exerts on the other after they have come to equilibrium magnitude directionSelect

Answer 1

Charges of the two sphere = Q_1 = -12nC Q_2 = -18 nC distance between Then = r = 0.270m a) Electric force exerted by one sphere on other = F = 1/4pi elementof_0 times Q_1 Q_2 /r^2 a_r = 1/4pi(1/36pi times 10^-9) times (-12)(-18) times 10^-18 /(0.270)^2 a_r = 9 times 10^9 times 2962.962 times 10^-18 a_r = 26666.66 times 10^-9 a_r = 26.666 times 10^-6 Newton = 26.66 mu N rightarrow As the two charges are of Same sign the force between Them is repulsive i.e. away the other Sphere. (b) when the two conductors are connected by a conducting wire the total charges will be Q_T = Q_1 + Q_2 = -12nC - 18nC = -30nC So charge on the each sphere = Q_T /2 = -30nC /2 = -15nC So (Q_1)_new = -15nC (Q_2)_new = -15 nC So force (F) = 1/4pi elementof_0 Q_1 Q_2 /r^2 a_r Newton = 9 times 10^9 times (-15 times 10^-9) (-15 times 10^-9)/(0.270)^2 Newton = 27777.77 times 10^-9 N = 27.77 mu N