Let a total charge 2 Q be distributed in a sphere of radius R , with the charge density given by ρ ( r ) = k r , where r is the distance from the centre. Two charges A and B , of - Q each, are placed on diametrically opposite points, at equal distance, a, from the centre. If A and B do not experience any force, then:

Step-by-step solution

As total charge on sphere is = 2 Q 2 Q = ∫ 0 R k r 4 π r 2 d r ⇒ k πr 4 = 2 Q Charged enclosed in the sphere of radius   a q = ∫ 0 a k r × 4 π r 2 d r = k π a 4 As force on   Q   is zero 1 4 π ε 0 × Q 2 2 a 2 = k π a 4 4 π ε 0 × a 2 × Q ⇒ Q 2 4 = k π a 4 Q = a 4 2 Q R 4 Q R 4 = 8 a 4 ⇒ R = 8 1 4   a or   a = 8 - 1 4 R