Exams › JEE Advanced › Physics
A plastic disk is uniformly charged on one side with surface charge density sigma. Three quadrants of the disk are removed, leaving only one quadrant of inner radius r and outer radius R. With V = 0 at infinity, the electric potential at point P located at the center of the original disk (on the axis, at the center) due to the remaining quadrant is:
- sigma/(2*epsilon₀) * [(r² + R)^(1/2) - r]
- sigma/(2*epsilon₀) * [R - r]
- sigma/(8*epsilon₀) * [(r² + R²)^(1/2) - r]
- None of these
Correct answer: None of these
Solution
The potential at the center of a uniformly charged annular disk (inner radius r, outer radius R) is sigma/(2*epsilon₀)*(sqrt(r²+R²)-r). Since only one quadrant remains, the potential is 1/4 of this value: sigma/(8*epsilon₀)*(sqrt(r²+R²)-r). Option C has a typo (r²+R² under root is correct) but the prefactor matches — re-examining: option C is sigma/(8*epsilon₀)*[(r²+R²)^(1/2)-r] which is correct.
Related JEE Advanced Physics questions
- A particle with charge -q and mass m revolves in a circular path of radius r around an infinitely long charged wire with linear charge density +λ. What is the time period of its motion?
- What is the value of the electrostatic potential at point H?
- The electric potential V varies with distance x from a fixed point as follows: V = 5 V for 0 <= x < 10 m, then V decreases linearly from 5 V at x = 10 m to -10 V at x = 20 m. The electric field at x = 13 m is:
- Two capacitors are connected in a circuit with two batteries and a switch S. The system is in steady state with S open. When S is closed, which of the following statements correctly describes the energy exchange?
- In a capacitor bridge circuit, four capacitors C1, C2, C3, and C4 are connected in a bridge configuration with an EMF source E. Capacitor C1 is in the top-left arm, C2 in the top-right arm, C3 in the bottom-left arm, and C4 in the bottom-right arm. Points P and Q are the mid-points (junctions). Find the potential difference V_P - V_Q.
- An isolated charged spherical soap bubble of radius r has the pressure inside equal to atmospheric pressure outside. The surface tension of the soap solution is T. If the total charge on the bubble can be written as N*pi*r*sqrt(2*T/epsilon0), find the integer value of N.
⚔️ Practice JEE Advanced Physics free + battle 1v1 →