Charge is distributed within a sphere of radius R with a volume charge density ρ r = A r 2 e - 2 r a ,…

Charge is distributed within a sphere of radius R with a volume charge density ρr=Ar2e-2ra, where A and a are constants. If Q is the total charge of this charge distribution, the radius R is:
  1. a2log11-Q2πaA
  2. alog11-Q2πaA
  3. alog1-Q2πaA
  4. a2log1-Q2πaA

Solution

ρr=Ar2 e-2ra



Charge enclosed between r and r+dr is

dq=ρr 4πr2dr

To get total charge Q

Q=0Rdq=0RAr2e-2r/a 4πr2dr=-4πAa2[e-2r/a]0R

Q=-4π Aa2e-2R/a-1

R=-ln1-Q24πAaa2=a2ln11-Q2πaA

Asked in: JEE Main 2019 (09 Jan Shift 2)

Practice more Electrostatics questions on Aicharya