Concept of Potential

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.