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A charge of magnitude Q is placed at a distance \(\dfrac{R}{3}\) from the center of a spherical shell of radius R, uniformly charged to the charge density σ. The electrostatic force on Q is: 
1. Proportional to σQ 
2. Proportional to \(\dfrac{\sigma}{Q}\)
3. Proportional to \(\dfrac{Q}{\sigma}\)
4. Zero

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Correct Answer - Option 4 : Zero

Ans: Option 4)

CONCEPT:

  • Gauss theorem: This theorem states that the surface integral of the normal component of the electric intensity E over a closed surface is always equal to \(\frac{1}{ϵ _{0}}\) times the total charge Q inside it.

\(E\times area= \frac{Q}{ϵ _{0}}\)

Where Q is the charge, ϵ0 is the permittivity of free space.

EXPLANATION:

  • Here the charge is laying inside the shell and having a radius R/3 smaller than the spherical shell radius R.
  • So as per Gauss' law, the electric field intensity is zero due to the charge enclosed by such a surface is zero because the charge density is at the surface of the sphere.
  • Therefore the net force is zero on the given charge.
  • correct option is 4).

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