Question

Consider 1 small sphere of radius R & n large spheres of radius NR each. Small sphere is touched to large spheres one by one. Charge on the nth large sphere is.

Small sphere : Charge Q and Radius R.
Large sphere: For all large spheres (N>1) initial Charge 0.

(a) (N/(N+1))^nQ

(b) (N/(N+1)^n)Q

(c) (N^n/(N+1))Q

(d) (N/(N+1))Q

Solution:

When two spheres are touched, their potential gets equal.

Suppose charge on first large sphere is q_1,

When small sphere touches the first large sphere, we get:

=> (k(Q-q_1))/R = (kq_1)/(NR)

=> q_1 = (NQ)/(N+1)

When it touches the second large sphere,

=> (k(Q-q_1-q_2))/R= (kq_2)/(NR)

=> q_2 = (NQ)/(N+1)^2

Similarly charge on nth large sphere,

 q_n =(NQ)/(N+1)^n

Therefore, option (b) is correct.