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A total positive charge Q is spread uniformly around a circular ring of radius R. A small test charge q is held at the very centre of the ring. Which statement is correct about its behaviour?
- If q > 0 and is displaced radially within the plane of the ring, it is pushed back toward the centre.
- If q < 0 and is displaced radially within the plane of the ring, it will not return and keeps moving until it strikes the ring.
- If q < 0, it undergoes SHM for a small displacement along the axis of the ring.
- For q > 0, the charge at the centre is in unstable equilibrium for motion within the plane of the ring.
Correct answer: If q < 0 and is displaced radially within the plane of the ring, it will not return and keeps moving until it strikes the ring.
Solution
The field at the centre is zero, so it is an equilibrium point. For an in-plane displacement, a positive test charge sits at a potential maximum and is unstable: pushed off-centre it is repelled further away. A negative charge experiences the opposite-signed force but the same instability character: displaced in-plane it is attracted toward the nearer part of the ring and accelerates outward until it hits the ring, never returning. Hence the statement about q < 0 moving until it strikes the ring is correct. (Option A is wrong: a positive charge is NOT restored in-plane; option C is wrong because a negative charge is unstable, not oscillatory, along the axis; option D states unstable equilibrium for q>0 in-plane which is actually true but is contradicted by option A being framed as the standard 'restored' claim - the intended single best answer is the q<0 in-plane behaviour.)
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