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Understanding Electrostatic Potential

71.A ball of ...

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71.A ball of radius R carries a positive charge whos volume charge density depends on the distance r from the centre of the ball as = [1-r/R]. Find the electric field at distance r>R

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Q. A ball of radius R carries a positive charge whose volume charge density depends only on the distance r from the ball's centre as:

ρ = ρ_{0} (1 - \frac{r}{R})

ρ_{0}

is constant. Assume

ϵ

as the permittivity of the ball.

Then the magnitude of the electric field as a function of the distance r outside the ball is given by :

Q. 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 = ρ_{0} (1 - r / R)

ρ_{0}

is a constant. Assuming the permittivities of the ball and the environment to be equal to unity, find:
(A) the magnitude of the electric field strength as a function of the distance

r

both inside and outside the ball;
(b) the maximum intensity

E_{m a x}

and the corresponding distance

r_{m}

Q. A sphere of radius R carries charge such that its volume charge density is proportional to the square of the distance from the centre. What is the ratio of the magnitude of the electric field at a distance 2R from the centre to the magnitude of the electric field at a distance of

\frac{R}{2}

from the centre

(i . e ., E_{r = 2 R} / E_{r = R / 2})

?

Q. 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 = ρ_{0} (1 - \frac{r}{R})

ρ_{0}

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.

Q. A non-conducting spherical ball of radius

R

contains a spherically symmetric charge with volume charge density

ρ = k r^{n}

r

is the distance from the centre of the ball and

n

is a constant. What should be

n

such that the electric field inside the ball is directly proportional to the square of distance from the centre?

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