JEE Advanced · 2014 · 25 May 2014 · Paper 2 · Electrostatics

Charges

Q, 2 Q

and

4 Q

are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii

R /2, R

and

2 R

, respectively, as shown in figure. If magnitudes of the electric fields at point P at a distance

R

from the center of spheres 1, 2 and 3 are

E_{1}, E_{2}

and

E_{3}

respectively, then

Answer: (C)

Solution

For sphere 1: Point P is outside (at distance

R

from center, radius

R /2

), so

E_{1} = \frac{k Q}{R ^{2}}

.

For sphere 2: Point P is on the surface (at distance

R

from center, radius

R

), so

E_{2} = \frac{k ( 2 Q )}{R ^{2}} = \frac{2 k Q}{R ^{2}}

.

For sphere 3: Point P is inside (at distance

R

from center, radius

2 R

). For a uniformly charged sphere, the field inside at distance

r

E = \frac{k Q r}{R ^{3}}

, so

E_{3} = \frac{k ( 4 Q ) R}{( 2 R ) ^{3}} = \frac{4 k QR}{8 R ^{3}} = \frac{k Q}{2 R ^{2}}

.

Comparing:

E_{2} = \frac{2 k Q}{R ^{2}}

E_{1} = \frac{k Q}{R ^{2}}

E_{3} = \frac{k Q}{2 R ^{2}}

.

Therefore,

E_{2} > E_{1} > E_{3}

JEE Advanced · 2014 · 25 May 2014 · Paper 2 · Single correct option