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Standard XII
Physics
Electric Field Due to Charge Distributions - Approach
Question

A system consists of a ball of radius R carrying a uniformly distributed charge q and surrounding space filled with a charge of volume density ρ=α/r where α is a constant and r is the distance from the centre of the ball. Find the charge on the ball for which the magnitude of electric field strength outside the ball is constant ? The dielectric constant of the ball and the surrounding may be taken equal to unity.

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Q1
A system consists of a ball of radius R carrying a uniformly distributed charge q and surrounding space filled with a charge of volume density ρ=α/r where α is a constant and r is the distance from the centre of the ball. Find the charge on the ball for which the magnitude of electric field strength outside the ball is constant ? The dielectric constant of the ball and the surrounding may be taken equal to unity.
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Q2
A system consists of a uniformly charged sphere of radius R and a surrounding medium filled by a charge with the volume density ρ=αr, where α is a positive constant and r is the distance from the centre of the sphere. Find the charge of the sphere for which the electric field intensity E outside the sphere is independent of R.
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A ball of radius R carries a positive charge whose volume density depends only on a separation r from the ball's centre as ρ=ρ0(1−r/R), where ρ0 is a constant. Assuming the permittivities of the ball and the environment to be equal to unity, find:
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A ball of radius R carries a positive charge whose volume density depends only on a separation r from the ball’s centre as ρ=ρ0(1−rR), where ρ0 is a constant. Assuming the permittivities of the ball and the environment to be equal to unity, find the ratio of the magnitude of the electric field strength inside the sphere to that of the outside.
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Q5
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