Question

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius R, with distance r from the centre O is represented by

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is A

The question involves understanding the variation of the electric field due to a uniformly charged insulating solid sphere with respect to the distance from its center. 

Let's analyze the behavior of the electric field inside and outside a uniformly charged solid sphere:

1. Inside the Sphere \((r < R)\):
   • The electric field \(E\) at a distance \(r\) from the center is given by: \(E = \frac{kQr}{R^3}\), where \(k\) is Coulomb's constant, \(Q\) is the total charge, and \(R\) is the radius of the sphere.
   • This indicates that the electric field increases linearly with distance from the center until \(r = R\).
2. Outside the Sphere \((r \geq R)\):
   • The sphere acts as a point charge, and the electric field \(E\) is given by: \(E = \frac{kQ}{r^2}\).
   • This implies that the electric field decreases with the square of the distance from the center.

Conclusion: The electric field increases linearly within the sphere and decreases with the square of the distance from the surface outward. This is represented by the correct graph in the options given.

Therefore, the correct graph representing this variation is the one where the electric field increases linearly from \(r = 0\) to \(r = R\) and then decreases as \(1/r^2\) for \(r \geq R\).