Two infinitely large sheets S1 and S2 having surface charge densities σ1 and σ2 (σ1 > σ2) respectively are placed at a distance d. Find the work done by the electric field when a charge particle ‘Q’ is displaced by a distance ‘a’ (a < d) at an angle 45° with the normal of the sheets. It is assume that the charge does not affect the surface charge densities of the two plates.
Answer & explanation
Correct answer: option 3
Force act along normal to the sheet so displacement is $\frac{d}{\sqrt 2}$ Work done $W= QE\frac{d}{\sqrt 2} =\frac{q\left(s_1-s_2\right)}{2 \sqrt{2}\epsilon_0} d$