Exams › JEE Main › Physics

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?

1. If q > 0 and is displaced radially within the plane of the ring, it is pushed back toward the centre.
2. 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.
3. If q < 0, it undergoes SHM for a small displacement along the axis of the ring.
4. 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.)

Related JEE Main Physics questions

• What is the SI unit of the permittivity of free space, ε₀?
• What is the SI unit used for electric flux?
• A constant electric field E is directed along the positive x-axis. If a charge of 0.5 C is displaced by 2 m along a line inclined at 60° to the x-axis, and the work done in this process is 10 J, what is the magnitude of the electric field?
• An electric dipole is located at the origin O along the x-axis. A point P lies 20 cm from O, and the line OP makes an angle π/3 with the x-axis. If the electric field at P is inclined at an angle θ to the x-axis, what is θ?
• A uniformly charged semicircular wire has radius a and linear charge density λ. The magnitude of the electric field at the centre of the semicircle is
• A point Q is located on the perpendicular bisector of an electric dipole whose dipole moment is p. If Q is at a distance r from the dipole and r is much greater than the dipole size, the electric field at Q varies as

⚔️ Practice JEE Main Physics free + battle 1v1 →