A charge Q is uniformly distributed throughout 25. the volume of a dielectric sphere of radius RI potential at its surface is 24 volts. Then potential R 3R 2 at r = and r= respectively are.?

Question

Answer

Calculating Potential of a Uniformly Charged Dielectric Sphere

Given:
- Charge Q is uniformly distributed throughout the volume of a dielectric sphere of radius R.
- The potential at the surface of the sphere, r = R, is 24 volts.

To Find:
- The potential at r = 3R.
- The potential at r = 2R.

Solution:

Electric Field Inside and Outside the Dielectric Sphere

For a uniformly charged sphere with volume charge density ρ, the electric field inside and outside the sphere is given by:
- Inside the sphere (r < r):='' e='' />₀)
- Outside the sphere (r > R): E = (Q/4πε₀r²)

Electric Potential Inside and Outside the Dielectric Sphere

The electric potential at a point P due to a charge Q is given by:
- V = (1/4πε₀) * (Q/r)
Using this formula, we can find the electric potential inside and outside the sphere:
- Inside the sphere (r < r):='' v='' />₀) * ((ρr²)/6)
- Outside the sphere (r > R): V = (1/4πε₀) * (Q/r)

Dielectric Constant and Electric Field

For a dielectric material with dielectric constant κ, the electric field inside the material is reduced by a factor of κ:
- E_inside = (E_vacuum/κ)

Electric Potential and Dielectric Constant

The electric potential inside a dielectric material with dielectric constant κ is also reduced by a factor of κ:
- V_inside = (V_vacuum/κ)

Finding the Potentials at r = 3R and r = 2R

Using the above formulas and the given values, we can find the potentials at r = 3R and r = 2R:
- At r = 3R:

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