For a charged spherical ball, electrostatic potential inside the ball varies with r as V = 2ar² + b. Here a and b are constants and r is the distance from the center. The volume charge density inside the ball is −λε. The value of λ is ________. Here ε is the permittivity of medium.
Physics · Circular Motion
JEE Mains 29 January 2023 Shift 2 Evening Shift

Question

For a charged spherical ball, electrostatic potential inside the ball varies with r as V = 2ar² + b. Here a and b are constants and r is the distance from the center. The volume charge density inside the ball is −λε. The value of λ is ________. Here ε is the permittivity of medium.

Physics · Circular Motion

G1 Physics · Accepted Answer

Electric field E = −dV/dr = −4ar. For a uniformly charged solid sphere, E = ρr/(3ε). Comparing, ρr/(3ε) = −4ar, so ρ = −12aε. Since ρ = −λaε, λ = 12.