Question

A spherical object of radius \( R \) is placed in a uniform electric field \( E \). If the dielectric constant of the material of the object is \( K \), find the induced charge on the surface of the object.

• A. \( K \cdot E \cdot R^2 \)
• B. \( \frac{K \cdot E \cdot R^2}{2} \)
• C. \( \frac{E \cdot R^2}{K} \)
• D. \( E \cdot R^2 \)

Hint:

The dielectric constant \( K \) affects how much charge is induced on a material when placed in an electric field. A higher \( K \) results in a greater induced charge.

Answer 1

The Correct Option is B

When a dielectric sphere is placed in a uniform electric field, the induced charge on the surface of the sphere is given by the formula: \[ Q = \frac{K \cdot E \cdot R^2}{2} \] Where: - \( K \) is the dielectric constant of the material, - \( E \) is the electric field, - \( R \) is the radius of the sphere. Thus, the induced charge on the surface of the sphere is \( \frac{K \cdot E \cdot R^2}{2} \).