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 i s ________. Here ε is the permittivity of medium.
Physics · Electrostatic · Electric Potential & Potential Energy
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 i s ________. Here ε is the permittivity of medium.

Physics · Electrostatic · Electric Potential & Potential Energy

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.