Exams › JEE Main › Physics

A uniform spherically symmetric surface charge is initially at rest, distributed on a sphere of radius R0. Due to mutual electrostatic repulsion the shell begins to expand. Which graph best represents the speed V of the expanding shell as a function of its instantaneous radius R(t)? (The shell starts at rest at R0, accelerates, and approaches a maximum terminal speed as R -> infinity.)

1. V starts from a nonzero value at R0 and decreases to zero as R increases
2. V starts at zero at R0, increases, and saturates to a constant maximum as R -> infinity
3. V increases linearly without bound as R increases
4. V starts at zero and increases without bound (no saturation) as R increases

Correct answer: V starts at zero at R0, increases, and saturates to a constant maximum as R -> infinity

Solution

The self-energy of a charged spherical shell is U = Q²/(8*pi*epsilon0*R). As the shell expands, U decreases and is converted to kinetic energy: (1/2)mV² = U(R0) - U(R) = (Q²/(8*pi*epsilon0))(1/R0 - 1/R). At R = R0, V = 0; as R increases, V increases; as R -> infinity, 1/R -> 0 so V approaches a finite maximum V_max = sqrt((Q²/(4*pi*epsilon0 m))(1/R0)). Thus V rises from zero and saturates to a constant value, matching the curve that starts at zero and levels off.

Related JEE Main Physics questions

• If an electric field vector E exists in a material whose dielectric constant is K, and ε0 denotes the permittivity of free space, which expression gives the electric displacement vector?
• If a unit positive charge is taken from point A to point B along the same equipotential surface, then what can be said about the potential difference V_A - V_B?
• Two thin metallic spherical shells are placed concentrically with radii R1 and R2, where R1 > R2. If the shells carry charges Q1 and Q2 respectively, what is the electric potential at a point located at distance r such that R2 < r < R1? (Take k = 1/(4πϵ0))
• An alpha particle is made to move through a potential difference of 10⁶ V. What kinetic energy does it gain?
• A parallel-plate capacitor has its entire gap filled with a dielectric whose dielectric constant changes with position x according to K(x) = K0 + λx, where λ is a constant. How is its capacitance C related to the vacuum capacitance C0?
• Two thin circular rings of radius R each are kept on the same axis with their centres separated by a distance d. One ring carries charge +q and the other carries charge −q. What is the potential difference between the centres of the two rings?

⚔️ Practice JEE Main Physics free + battle 1v1 →