Work done to move a charge

Calculate the work done in moving a charge q from i) A to B and from ii) A to C as shown in the figure, The radius of the sphere is R and point B is at a distance of r from the centre O of the sphere and A and C are  points inside the sphere, the Charge enclosed by the sphere is Q

Let the potential at A is V_A and that of B is V_B

the work done is W_AB=q(V_B-V_A)

Note: 1) Potential inside the sphere is a constant= potential on the surface of the sphere

           2)Since electric field E=dv/dl =d(constant)/dl=0 ie field inside the sphere is zero

           3) Thus E=0 inside a charged sphere and is known as Electrstatic shielding

i) V_A=(1/4πε₀) Q/R

   V_B=(1/4πε₀) Q/r
W_AB=q (V_B -V_A)

W_AB=(1/4πε₀) Qq[(1/r)-(1/R)]

•^••W_AB=(Q q/ 4πε₀) [(R-r)/Rr]

ii) W_AC=q(V_C-V_A)

inside the sphere the potential is the same ie V_C=V_A

•^•• W_AC=0

Prepared by Sai’s Classes Poonkunnam Thrissur +919846088761