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Manipal MET2016PhysicsCapacitance

A thin dielectric rod of length l lies along X -axis. One end of the rod is placed at the origin and the other end of the rod is placed at (l, 0) . A total charge Q is distributed uniformly along the length of the rod. What is the potential at a point (x, 0) when x 1 ?

Options

  1. AQ 4 ₀ _e ( x x-1 )
  2. BQ 4 ₀ l _ ( x l )
  3. CQ 4 ₀ l _e ( x-l x )
  4. DQ 4 ₀ l

Correct answer

C. Q 4 ₀ l _e ( x-l x )

Step-by-step solution

The potential due to a small element of length d r having charge d Q of the dielectric rod is given by d V= d Q 4 ₀ r or d V= d r 4 ₀ r [ array c = d Q d r , d r=d Q array ] or V= 4 ₀ _x^ x-l d r r aligned & = 4 ₀ [ _e r ]_x^ x-l & = 4 ₀ ( x-l x ) aligned V= Q 4 ₀ 1 e ( x-l x ) When = Q l (for whole length of rod)

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