For a non - conducting charged solid sphere of radius R. Which of the following graph shows the variation of electric field with increasing distance r from the center?

  1. F1 Jitendra Kumar Anil 12.02.21 D13
  2. F1 Jitendra Kumar Anil 12.02.21 D14
  3. F1 Jitendra Kumar Anil 12.02.21 D15
  4. F1 Jitendra Kumar Anil 12.02.21 D16

Answer (Detailed Solution Below)

Option 2 : F1 Jitendra Kumar Anil 12.02.21 D14
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Detailed Solution

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CONCEPT:

Gauss's law:

  • According to Gauss law, the total electric flux linked with a closed surface called Gaussian surface is \(\frac{1}{ϵ_o}\) the charge enclosed by the closed surface.

\(⇒ ϕ=\frac{Q}{ϵ_o}\)

Where ϕ = electric flux linked with a closed surface, Q = total charge enclosed in the surface, and ϵo = permittivity​

EXPLANATION:

F15 Prabhu 26-4-2021 Swati D3

Case 1:

  • The electric field intensity at a point inside a non - conducting charged solid sphere of radius R is given by


\(⇒ E = \frac{r\rho}{3\epsilon}\)     ...1)

Here, ϵ = electrical permittivity of the material of the insulating sphere, q' = charge enclosed by a sphere S, and r = radius of a sphere S

  • From the above, it is clear that the electric field intensity at a point inside a non - conducting charged solid sphere varies directly proportional to the distance of the point from the centre of the sphere


Case 2:

  • At the centre of the sphere, r = 0, the electric field intensity at a point inside a non - conducting charged solid sphere of radius R is zero.


Case 3:

  • At the surface of the sphere, r = R


\(⇒ E = \frac{r\rho}{3\epsilon}= maximum\)

Case 4:

  • At the surface outside the sphere, r > R


\(⇒ E = \frac{q}{4\pi ϵ _0 r^2}\)

  • From the above, it is clear that the electric field intensity at a point outside a non - conducting charged solid sphere varies inversely proportional to the distance of the point from the centre of the sphere.
  • The correct graph shows that shows the variation of the electric field with increasing distance r from the center


F15 Prabhu 26-4-2021 Swati D4

Hence option 2 is correct.

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