Electric Field at a Distance of 3 cm from the Center of a Dielectric Sphere

To determine the electric field at a distance of 3 cm from the center of a dielectric sphere, we need to consider the properties of the dielectric material and the relationship between the electric field and distance from the center of the sphere.

Given information:
- Distance from the center of the sphere, r₁ = 20 cm = 0.2 m
- Radius of the dielectric sphere, R = 10 cm = 0.1 m
- Electric field at a distance of 20 cm from the center, E₁ = 100 V/m

Electric Field and Distance Relationship:
The electric field inside a uniformly charged sphere is given by the equation:
E = k * Q * r / (R³ * ε)

Where:
- E is the electric field
- k is the Coulomb constant (9 x 10⁹ Nm²/C²)
- Q is the total charge of the sphere
- r is the distance from the center of the sphere
- R is the radius of the sphere
- ε is the permittivity of the dielectric material

Calculating the Total Charge:
Since the dielectric sphere is uniformly charged, we can calculate the total charge using the equation:
Q = (4/3) * π * R³ * σ

Where:
- σ is the charge density

Calculating the Electric Field at a Distance of 3 cm:
We need to find the electric field at a distance of 3 cm from the center, which is denoted as E₂.
Using the equation for the electric field, we can rearrange it to solve for E₂:
E₂ = E₁ * r₁ * (R³ * ε) / (r₂ * (R³ * ε))

Substituting the given values:
E₂ = 100 V/m * 0.2 m * (0.1 m)³ * ε / (0.03 m * (0.1 m)³ * ε)

Simplifying the Equation:
Since the dielectric constant (ε) is the same for both distances, it cancels out in the equation. Therefore, the value of ε does not affect the electric field at the distance of 3 cm.

E₂ = 100 V/m * 0.2 m / 0.03 m

Calculating the Electric Field:
E₂ = 2000 V/m / 0.03 m

E₂ = 66666.67 V/m

Therefore, the electric field at a distance of 3 cm from the center of the dielectric sphere is approximately 66666.67 V/m.

If the electric field at a distance of 20cm from the centre of a dielectric sphere of radius 10cm is, 100V/m. Then E at 3cm distance from the centre of sphere is Electric field=kq/d^2 Where 'd' is the distance from the centre Electric field at a distance of 20 cm(E1)=kq/20^2 Electric field at a distance of 20 cm(E2)=kq/3^2 E1/E2=3^2/20^2 but E1 is given and E1=100 V/m 100/E2=3^2/20^2 E2=20^2*100/3^2=4.444 x 10 V/m Therefore, E at 3cm distance from the centre of sphere is 4.444 x 10^3 V/m.