Potential inside a hollow sphere is:

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Agniveer Vayu Group X 14 Oct 2023 Shift 1 Memory Based Paper
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  1. constant
  2. proportional to distance from centre
  3. inversely proportional to the distance
  4. inversely proportional to square of distance

Answer (Detailed Solution Below)

Option 1 : constant
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Detailed Solution

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CONCEPT:

Electrical potential:

  • The electric potential at any point in the electric field is defined as the amount of work done in moving a unit positive test charge from infinity to that point without acceleration.

\(\Rightarrow V=\frac{kq}{r}\)

Electrical potential difference: 

  • In an electrical field, the potential difference between two points (V) is defined as the amount of work done (W) by an external agent in moving a unit charge from one point to another.
  • It is given as:

\(⇒ \Delta V=\frac{W}{Q}\)

Where W = Work done, Q = Charge, ΔV = Electrical potential difference, V = electric potential at a point, k = 9×109 N-m2/C2, q = charge, and r = distance of a point from the center of the charge

CALCULATION:

  • Since in a hollow sphere, the charge is only present at the surface, so the electric field intensity inside the hollow sphere is zero.
  • So it is not required to do work done on a unit positive test charge from one point to another inside the hollow sphere.
  • Hence potential inside a hollow sphere is constant (\(\Rightarrow V=\frac{kq}{r}\)).
  • Hence, option 1 is correct.
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