Question

Four identical point charges (+4.0 µC) are placed at the corners of a square which has 20- cm sides. How much work is required to assemble this charge arrangement starting with each of the charges a very large distance from any of the other charges?

Answer 1

The  work required to assemble this charge arrangement starting with each of the charges as very large distance from any of the other charges is +1.9 J.

Work done

The work required to assemble this charge arrangement starting with each of the charges as very large distance from any of the other charges is calculated as follows;

W = qV

where;

• V is the potential energy
• q is the charge

$W = q (\frac{kq}{r} )$

where;

• r is the distance of separation of the charges

• Distance between two diagonal of a square = r√2

$W = q (\frac{kq}{r} + \frac{kq}{r\sqrt{2} } + \frac{kq}{r} )\\\\W = \frac{kq^2}{r} ( 2 + \frac{1}{\sqrt{2} } )\\\\W = \frac{(9\times 10^9 \times (4\times 10^{-6})^2}{0.2} ( 2.707)\\\\W = 1.9 \ J$

Thus, the  work required to assemble this charge arrangement starting with each of the charges as very large distance from any of the other charges is +1.9 J.

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