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Potential at a Point Due to a Dipole

Let P(r)=(Q*r...

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Let P(r)=(Q*r)/R4 be the charge density distribution for solid sphere of radius R & total charge Q. for a point p,inside a sphere at a distance r1from centre of sphere,the magnitude of electric field is?

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P (r) = \frac{Q}{π R^{4}} r

be the charge density distribution for a solid sphere of radius

R

and total charge Q. For a point

p_{1}

inside the sphere at distance

r_{1}

from the centre of sphere, the magnitude of electric field is

ρ (r) = \frac{Q r}{4 π R^{4}}

be the charge density distribution of a solid sphere of radius

R

and total charge

Q

. Find the magnitude of electric field at a point

P

inside the sphere at a distance

r_{1}

from the centre of the sphere.

Q. A solid nonconducting sphere of radius

R

has a uniform charge distribution of volume charge density,

ρ = ρ_{0} \frac{r}{R}

ρ_{0}

is a constant and r is the distance from the centre of the sphere. Show that:
(a) the total charge on the sphere is

Q = π ρ_{0} R^{3}

(b) the electric field inside the sphere has a magnitude given by,

E = \frac{K Q r^{2}}{R^{4}}

Q. An insulating solid sphere of radius

R

has a uniform volume charge density and total charge

Q

. Find the electric field at a point outside the sphere at a distance of

r

from its centre.

Q. A charge Q is distributed uniformly in a sphere (solid). Then the electric field at any point r where r < R (R is radius of the sphere) varies as

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