Question

A square is placed with its centre at origin and having sides parallel to $x$ and $y-$ axes. It has surface charge density $\sigma (x,y)={\sigma }_{0}xy$ within its boundaries. The charge of each side of square is $Q$ . The total charge on the square is:

• A. $2{\sigma }_0{Q}^2$
• B. $4{\sigma }_0{Q}^3$
• C. ${\sigma }_0{Q}^2$
• D. Zero

Answer 1

The correct option is B $4{\sigma }_0{Q}^3$

The surface charge density is given as

$\sigma =\frac{q}{A}$

Let the side of the square be$2a$

The area of the square is$4a^2$

Hence the charge density on the surface will be

$q=4{\sigma }_0{a}^2$