A sphere of radius r has a electric charge uniformly distributed in its entire volume. At a distance d from the center inside the sphere (d?

Question

Answer

Electric Field Inside a Charged Sphere

When an electric charge is uniformly distributed throughout the volume of a sphere, the electric field inside the sphere can be calculated using Gauss's Law.

Gauss's Law

Gauss's Law states that the flux of the electric field through a closed surface is equal to the net charge enclosed by the surface divided by the permittivity of free space.

Calculation of Electric Field Inside the Sphere

Consider a sphere of radius r with a charge Q distributed uniformly throughout its volume. Let us assume that we are interested in finding the electric field at a distance d from the center inside the sphere.

We can choose a Gaussian surface in the form of a sphere of radius d with its center at the center of the original sphere.

Since the charge is uniformly distributed throughout the volume of the sphere, the charge enclosed by the Gaussian surface is proportional to the volume of the sphere enclosed by the surface.

The electric field at any point on the Gaussian surface is perpendicular to the surface, and hence, the electric flux through the surface is given by:

Flux = E x 4πd²

where E is the electric field at a point on the Gaussian surface.

Using Gauss's Law, we can write:

Flux = Q / ε₀

where ε₀ is the permittivity of free space.

Equating the two expressions for Flux, we get:

E x 4πd² = Q / ε₀

which gives the electric field inside the sphere as:

E = Q / (4πε₀d²)

Thus, the electric field inside a uniformly charged sphere is inversely proportional to the square of the distance from the center.

Conclusion

The electric field inside a uniformly charged sphere is inversely proportional to the square of the distance from the center. This relationship is similar to the inverse square law that governs the behavior of gravity.

Similar Class 11 Doubts

A uniform ring of mass M and radius R is placed directly above uniform sphere of mass 8M and of same radius R. The centre of the ring is at a distance of d = 3R from the centre of sphere. The gravitational attraction between the sphere and the ring is

A sphere of mass m and radius has a concentric cavity of radius r1 .The force f exerted by the sphere on a particle of mass m located a distance r from the centre of the sphere varies as 0

four identical spheres of radius 10cm and mass 10kg are placed on a horizontal.surface touching one another so that their centres are located at the corners of square of side 20cm .what is the distance of their centre of mass from centre of sphere

From a uniform circular disc of radius R,a circular disc of radius R/6 and having center of a distance R/2 from the centre of the disc is removed. Determine the centre of mass of remaining portion of the disc?

A boy walks uniformly along the sides of a rectangular Park of size 400 m×300 m starting from one corner to the other corner diagonally opposite. Which of the following statement is correct? (

Top Courses for Class 11View all

Chemistry Class 11

CUET Mock Test Series

English Class 11

Chemistry Practice Tests: CUET Preparation

CUET Mock Test: Humanities Subjects 2025

Top Courses for Class 11

Top Courses for Class 11

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams