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In a spherical distribution, the charge density varies as ρ r = A r for a < r < b (as shown) where A is a constant. A point charge Q lies at the centre of the sphere at r = 0 . The electric field in the region a < r < b has a constant magnitude for

Options

  1. AA = 0
  2. BA = Q
  3. CA = Q 2 π a 2
  4. DA = Q 4 &pi; a 2

Correct answer

C. A = Q 2 π a 2

Step-by-step solution

Q in = &#8747; a r A r &#215; 4 &#960; r 2 dr + Q = 2 &#960; A r 2 - a 2 + Q E = Q in 4 &#960;r 2 &#949; 0 &#8658; E = A 2 - a 2 A 2r 2 + Q 4 &#960;r 2 &#949; 0 For E = constant, - a 2 A 2r 2 + Q 4 &#960; r 2 = 0 &#8658; A = Q 2 &#960; a 2

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