As the
potential on equipotential surface does not change
$$\mathrm{So}\left(\mathrm{V}_{2}-\mathrm{V}_{1}\right)=0$$
And $$w=\left(V_{2}-V_{1}\right)
q$$
So, work
done on moving a charge is zero, verifies answer (c).
We know the
work done by charge $$q$$ in moving in electric field.
$$\mathrm{dW}=\mathrm{F}
\cdot \mathrm{dl}$$
$$\int=\int
q E d l$$
$$\mathrm{W}=\mathrm{q}
\cdot \int E \cdot d l$$
So, $$W \neq
\int E . d l$$ or answer (b) is wrong.
Answer (a)
and (b) can be true only when $$\mathrm{q}=+ 1 \mathrm{C}$$ which is not given
in question.