As shown in the figure a square having length a has electric charge distribution of surface charge density `sigma =sigma_(0)xy`. The total electric charge on the square will be......(The cartesian coordinate system is shown in figure.)

Explanation

Consider an element of area dxdy at a point [x, y) as shown in the figure. The charge on the area element is:
`dq = sigma_(0).xy dx.dy`
`therefore` Therefore, total electric charge on the surface.
`Q = sigma_(0)int_(0)^(a)x.dx.int_(0)^(a)ydy`
`=sigma_(0)[x^(2)/2]_(0)^(a).[y^(2)/2]_(0)^(a)`
`therefore =(sigma_(0)a^(4))/4`