The electric potential on the surface of a charged spherical conductor of radius (5 ~cm ) is (200 ~V ). Work done in moving a charge of (+5 C ) from a point (A ) to another point (B ) situated at distances of (15 ~cm ) and (10 ~cm ) respectively from the centre of the sphere is

Step-by-step solution

Electric potential on the surface of sphere, (V=200 ~V ) Radius, (R=5 ~cm =5 10⁻² ~m ) Charge, (q=5 C ) Electric potential on the surface of sphere, ( aligned V & =9 10^9 Q R 200 & =9 10^9 Q 5 10⁻² Q= 10⁻⁸ 9 C aligned ) Work done to move the charge from point (A ) to point (B ) is given as ( aligned W & =V_ A B q & = (V_B-V_A ) q= (9 10^9 Q r_B -9 10^9 Q r_A ) 5 & =9 10^9 ( 10⁻⁸ 9 10⁻¹ - 10⁻⁸ 9 15 10⁻² ) 5 & =45 10^9 10⁻⁸ [ 1 9 10⁻¹ - 1 9 15 10⁻² ] aligned ) ( aligned & =450 1 9 [10- 100 15 ]=50 [ 50 15 ] & =166.66