Electric field due to a uniformly charged hollow sphere at a distance of r (where r is greater than the radius of the sphere) is __________a)Proportional to rb)Inversely proportional to rc)Proportional to r2d)Inversely proportional to r2Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Explanation:
The electric field due to a uniformly charged hollow sphere at a distance of r from the center of the sphere can be found using Gauss's law. Gauss's law states that the electric flux through any closed surface is proportional to the charge enclosed within that surface.

Electric field inside the hollow sphere:
The electric field inside the hollow sphere is zero as the charge is distributed uniformly on the surface of the sphere and there is no net electric field inside the sphere.

Electric field outside the hollow sphere:
Consider a Gaussian surface in the form of a sphere of radius r (where r is greater than the radius of the sphere) centered at the center of the hollow sphere. The charge enclosed within this surface is equal to the total charge on the hollow sphere.

Q = 4πε0R2σ

where Q is the total charge on the sphere, R is the radius of the sphere and σ is the surface charge density.

Using Gauss's law, the electric field outside the sphere can be calculated as:

Φ = EA = Q/ε0

where Φ is the electric flux, A is the area of the Gaussian surface and E is the electric field.

Substituting the value of Q, we get:

E = Q/(4πε0r2) = σr/(ε0)

where r is the distance from the center of the sphere to the point at which the electric field is to be calculated.

r is greater than R, therefore we can approximate the surface charge density σ as:

σ = Q/4πR2

Substituting this value in the above equation, we get:

E = Q/(4πε0r2) = Q/(4πε0R2) * R2/r2 = σR2/r2

Therefore, the electric field due to a uniformly charged hollow sphere at a distance of r (where r is greater than the radius of the sphere) is inversely proportional to r2.

Answer: d) Inversely proportional to r2.

Answer

If the total charge of the sphere is q then the electric field at a distance of r is equal to

Therefore the electric field is proportional is (1/(r²)) (if r > radius of the sphere). But if r < radius of the sphere the electric field will be zero i.e. electric field inside a hollow sphere is always zero.

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