7. A square PQRS is of side a. Four charges are to be
placed at the corners as shown in the figure. Find
the work done in placing charges at P, Q, R and S
in steps respectively as well as total work done.
Will some work be done to bring a charge to the
centre of the square ?
Answers
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Work done = -q²/4πε°d (4 - √2)
Explanation:
PR = QS = √(PQ² + QR²) = √d² + d² = √2d²
Total Work done = PE of 4 charges
= 1/ 4πε° [(q *-q)/d + (-q*q)/d + (q*-q)/d + (-1*q)/d]
= 1/ 4πε°d (√2 - 4 q²)
= -q²/4πε°d (4 - √2)
Extra work needed = charge * potential at E due to charges at four corners
W = q° * (q-q+q-q) / [4πε°d (√2/2)] = 0
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