The region between two concentric spheres of radii 'a' and 'b', respectively (see figure),…

The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density ρ=Ar , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is:

  1. 2Qπa2-b2
  2. 2Qπa2
  3. Q2πa2
  4. Q2πb2-a2

Solution

E=E1+E2

⇒E=KQ+ar4πx2dxAxr2

E=KQr2+4πAr22r2-a22r2

dEdr=0

-2Qr3+8πAa22r3=0

A=Q2πa2

Asked in: JEE Main 2016 (03 Apr)

Practice more Electrostatics questions on Aicharya