The work done to move a charge along an equipotential from `A` to `B`

Options

A. cannot be defined as `- int_(A)^(B) vec(E ) vec(dl)`
B. must be defined as `- int_(A)^(B) vec ( E). vec(dl)`
C. is zero
D. can have a non-zero value

Answer

B, C

Explanation

Work done to move a charge `q` from `A` to `B` along an equipotential surface,
`W=q(V_(B)-V_(a))q int_(A)^(B) dV=-q int_(A)^(B) vec(E). vec(dl)`
Also, for an equipotential surface, `V_(A) = V_(B) = Constant`
`:. W =0`.