Question

If charge is distributed uniformly in xy plane with charge density $+\sigma$ in first quadrant and $-\sigma$ in remaining three quadrants, then work done by electric field in moving a point charge q from (0, 0, d) to (0, 0, 2d) is

• A. $\frac{-\sigma q}{4{\epsilon }_0}d$
• B. $\frac{\sigma q}{4{\epsilon }_0}d$
• C. $\frac{-\sigma }{2{\epsilon }_0}qd$
• D. $\frac{\sigma q}{{\epsilon }_0}d$

Answer 1

The correct option is A $\frac{-\sigma q}{4{\epsilon }_0}d$

The distance between them $=2d-d=d$

The charge density $=\sigma$

Now, work done $=F.d$ $=\frac{-\sigma q}{4{ϵ}_0}.d$

Now $(-ve)$ since for the left hand side of the $y$ axis.