Question

A square of side b centred at the origin with sides parallel to axes x and y has surface charge density σ(x,y) =kxy (where k is a constant ) within its boundaries. Total charge on the square is?
Ans given is zero . Please elaborate on how to get zero

Answer 1

Thus the surface charge density is 4σa^2

Explanation:

Given data:

• Surface charge density = σ
• Side of Square = b
• To find: Charge on square = Q = ?

Solution:

We know that:

Surface charge density = σ = q / A

Side of square = 2 a

Area of Square = side of square × side of square

Area of Square = 2a x 2a = 4 a^2

The charge density = 4σa^2

Thus the surface charge density is 4σa^2

Answer 2

Given that,

Centered side at origine = b

Surface charge density $\sigma(x,y)=k(x,y)$

Let the side of the square be 2b.

We need to calculate the area of square

Using formula of area

$A = (side)^2$

Put the value into the formula

$A=(2b)^2$

$A= 4b^2$

We need to calculate the charge on the square

Using formula of  surface charge density

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

$q=\sigma A$

Where, q = charge

A = area of square

Put the value into the formula

$q=\sigma\times 4b^2$

$q=4\sigma b^2$

Hence, The charge on the square is $4\sigma b^2$