Question 151: Electrostats & Capacitance

Question

Charges $$Q,$$ $$2Q$$ and $$4Q$$ are uniformly distributed in three dielectric solid spheres $$1,2$$ and $$3$$ of radii $$R/2,R$$ and $$2R$$ respectively, as shown in figure. If magnitude of the electric fields at point $$P$$ at a distance $$R$$ from the center of sphere $$1,2$$ and $$3$$ are $${E_1}$$, $${E_2}$$ and $${E_3}$$ respectively, then

Accepted Answer

Electric field due to uniformly charged dielectric solid sphere of radius R at a point P is given by
$$E = \left\{ {\matrix{
   {k\,.\,{Q \over {{R^3}}}\,.\,r,} & {r \le R}  \cr 
   {k\,.\,{Q \over {{r^2}}},} & {r > R}  \cr

} } \right.$$
In first two cases, P is outside the sphere. Therefore,
$${E_1} = {1 \over {4\pi {E_0}}}.\,{Q \over {{R^2}}}$$ ..... (1)
$${E_2} = {1 \over {4\pi {E_0}}}.\,{{2Q} \over {{R^2}}}$$ .... (2)
In Sphere 3, point P located is inside. Therefore,
$${E_3} = \left( {{\rho  \over {3{E_0}}}} \right)r$$
$$\rho  = {{4Q} \over {(4/3)\pi {{(2R)}^3}}}$$
$$ = {{12Q} \over {4\pi \,.\,8{R^3}}} = {{3Q} \over {8\pi }}$$
$${E_3} = \left( {{{3Q} \over {\pi {R^3}}}} \right)R$$
$${E_3} = {1 \over {4\pi {E_0}}}\,.\,{Q \over {2{R^2}}}$$ ..... (3)
$${E_2} > {E_1} > {E_3}$$

Answer

$${E_1} > {E_2} > {E_3}$$

Answer

$${E_3} > {E_1} > {E_2}$$

Answer

$${E_2} > {E_1} > {E_3}$$

Answer

$${E_3} > {E_2} > {E_1}$$

Electrostats & Capacitance

Charges $Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1,2 and 3 of radii R/2,R and 2R respectively, as shown in figure. If magnitude of the electric fields at point P at a distance R from the center of sphere 1,2 and 3 are {E_1}, {E_2} and {E_3}$ respectively, then

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