JEE Advanced 2014 · Paper 2 · Physics Q4

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PhysicsSingle correct+3 / -1Question 4 of 60

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 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

Three uniformly charged dielectric spheres: sphere 1 (radius R/2, charge Q) with P outside at distance R from its centre; sphere 2 (radius R, charge 2Q) with P on its surface; sphere 3 (radius 2R, charge 4Q) with P inside at distance R from its centre.

E_1>E_2>E_3

E_3>E_1>E_2

E_2>E_1>E_3

E_3>E_2>E_1

Answer and worked solution

Official answer: C

Let $k=\frac1{4\pi\varepsilon_0}$ .

Sphere 1 (P outside): $E_1=\dfrac{kQ}{R^2}$ .
Sphere 2 (P on the surface): $E_2=\dfrac{k(2Q)}{R^2}$ .
Sphere 3 (P inside, uniform charge): $E_3=\dfrac{k(4Q)R}{(2R)^3}=\dfrac{kQ}{2R^2}$ .

So $E_2>E_1>E_3$ .

(C)

Topics:Electric flux and Gauss's law Electric field

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JEE Advanced 2014 · Paper 2, Physics question 4