Two identical metallic spheres A and B when placed at certain distance in air repel each other with a force of F . Another identical uncharged sphere C is first placed in contact with A and then in contact with B and finally placed at midpoint between spheres A and B . The force experienced by sphere C will be :

Step-by-step solution

Let charge on A and B be q A = q B = q . Then force acting between them is F = K q 2 r 2 . When C is placed in contact with A , charge on A and C will be = q 2 Now C is placed in contact with B , charge on B and C will be = q + q 2 2 = 3 q 4 Now, force experienced by sphere C is F ' = F 2 - F 1 = K 9 q 2 16 × r 2 4 - K 3 q 2 8 × r 2 4 = K 3 q 4 - K q 2 r 2 4 × 3 q 4 = 3 K q 2 4 r 2 = 3   F 4