Question

Two equally charged, identical metal spheres A and B repel each other with a force 'F'. The spheres are kept fixed with a distance 'r' between them. A third identical, but uncharged sphere C is brought in contact with A and then placed at the mid-point of the line joining A and B. The magnitude of the net electric force on C is

• A. F
• B. 3F/4
• C. F/2
• D. F/4

Answer 1

Answer: (A)

F

Answer 2

Initially

$F = k\frac{Q^{2}}{r^{2}}$ ....... (i)

Finally

Force on C due to A,

$F_{A} = \frac{k(Q/2)^{2}}{(r/2)^{2}} = \frac{kQ^{2}}{r^{2}}$

Force on C due to B,

$F_{B} = \frac{KQ(Q/2)}{(r/2)^{2}} = \frac{2KQ^{2}}{r^{2}}$

∴ Net force on C, $F_{net} = F_{B} - F_{A} = \frac{kQ^{2}}{r^{2}} = F$