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A uniformly charged solid sphere of radius R has potential V 0 (measured with respect to ∞ ) on its surface. For this sphere the equipotential surfaces with potential 3 V 0 2 , 5 V 0 4 , 3 V 0 4 and V 0 4 have radius R 1 , R 2 , R 3 and R 4 respectively. Then Note : This question had two option correct at the time of examination. Proper corrections are made in the question to avoid it.

Options

  1. A2 R > R 4
  2. BR 1 = 0 and R 2 > R 4 - R 3
  3. CR 1 ≠ 0 and R 2 - R 1 > ( R 4 - R 3 )
  4. DR 1 = 0 and R 2 < R 4 - R 3

Correct answer

D. R 1 = 0 and R 2 < R 4 - R 3

Step-by-step solution

Potential for uniformly charged solid sphere v = 1 4 &#960; &#949; 0 Q r outside i.e r > R v = 1 4 &#960; &#949; 0 Q R on the surface v = 1 4 &#960; &#949; 0 Q R 3 2 - 1 2 r 2 R 2 inside i.e. r < R Clearly &#160;&#160; 3 v 0 2 , 5 v 0 4 are inside potentials &#8757; &#62; v 0 3 v 0 4 , v 0 4 are outside potentials &#8757; &#60; v 0 To get R 1 : 3 v 0 2 = 1 4 &#960; &#949; 0 Q R 3 2 - 1 2 R 1 2 R 2 where, v 0 = 1 4 &#960; &#949; 0 Q R 3 2 &#215; 4 &#960; &#949; 0 Q R = 1 4 &#960; &#949; 0 Q R 3 2 - 1 2 R 1 2 R 2 3 2

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