Four point charges \(q_A\)\( = 2 µC\), \(q_B\) \(= −5 µC\), \(q_C\) = 2 µC, and \(q_D\) \(= −5 µC\) are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of 1 µC placed at the centre of the square?
Four point charges \(q_A\)\( = 2 µC\), \(q_B\) \(= −5 µC\), \(q_C\) = 2 µC, and \(q_D\) \(= −5 µC\) are located at the corners of a square ABCD of side 10 cm. What is the force on a charge of 1 µC placed at the centre of the square?
Solution and Explanation
The given figure shows a square of side 10 cm with four charges placed at its corners. O is the centre of the square.
Where,
(Sides) AB = BC = CD = AD = 10 cm
(Diagonals) AC = BD = \(10\sqrt 2\) cm
AO = OC = DO = OB = \(5\sqrt 2\) cm
A charge of amount 1µC is placed at point O.
Force of repulsion between charges placed at corner A and centre O is
equal in magnitude but opposite in direction relative to the force of repulsion
between the charges placed at corner C and centre O. Hence, they will cancel
each other. Similarly, force of attraction between charges placed at corner B
and centre O is equal in magnitude but opposite in direction relative to the
force of attraction between the charges placed at corner D and centre O.
Hence, they will also cancel each other. Therefore, net force caused by the
four charges placed at the corner of the square on 1 µC charge at centre O is
zero.
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