A charge 'q' is placed at the centre of the line joining two equal charges 'Q'. The system of three charges will be in equilibrium if q is equal to:
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A charge 'q' is placed at the centre of the line joining two equal charges 'Q'. The system of three charges will be in equilibrium if q is equal to:

G1 Physics · Accepted Answer

Step 1: The middle charge experiences zero net force by symmetry. Step 2: If adjacent separation is r, two end charges are 2r apart. Step 3: On an end charge, repulsion due to the other end charge = kQ²/(2r)². Step 4: Middle charge must attract: kQ|q|/r² = kQ²/(4r²) ⇒ q = −Q/4.