Four point charges each having charge Q are located at the corners of a square having sides of length a. Find symbolic expressions for the work required to bring a fifth charge q from infinity to the center of the square.

Explanation:

We shall first calculate electric potential at the centre of square due to four charges of Q .

potential = k Q / r , k = 9 x 10⁹ , Q is charge which is placed at distance r from the point where potential is measured .

Distance of corner of square to centre = √ 2 a / 2 = a / √2 = .707 a

potential due to one charge

= k x Q / .707 a

= 9 x 10⁹ x Q / .707a

= 12.73 x 10⁹ Q/a

Potential due to 4  charges

= 4 x 12.73 x 10⁹ Q/a

= 50.92 x 10⁹ Q/a .

Potential at infinity = 0

Work done in carrying charge q from infinity to centre of square

= potential difference x charge

= ( 50.92 x 10⁹ Q/a - 0 ) x q

= 50.92 x 10⁹ x Qq / a  J .

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