Please show work and expalin Thank you Four conducting spher

Please show work and expalin. Thank you.

Four conducting spheres: A, B, C, and D have charges: 1 nC, -2 nC, 4 nC, and -5 nC respectively. If: 1) A and B touch and separate, 2) A and C touch and separate, 3) B and D touch separate, and finally 4) C and D touch and separate, what is the total and individual charges on the spheres?

Solution

After 1

charge on A = [1 + (-2)]/2 = - 0.5 nC

charge on B = [1 + (-2)]/2 = - 0.5 nC

After 2

Charge on A = [-0.5 + 4 ]/2 = 1.75 nC

Charge on C = [-0.5 + 4 ]/2 = 1.75 nC

After 3

Charge on B = [-0.5 + (-5)]/2 = -2.75 nC

Charge on D = [-0.5 + (-5) ]/2 = -2.75 nC

After 4

Charge on C = [1.75 + (-2.75)]/2 = -0.5 nC

Charge on D = [1.75 + (-2.75)]/2 = -0.5 nC

Total charge = 1.75 + (-2.75) + (-0.5) + (-0.5) = -2.0 nC