JEE Advanced 2015 · Paper 2 · Physics Q11

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PhysicsMultiple correct+4 / -2Question 11 of 60

Consider a uniform spherical charge distribution of radius $R_1$ centred at the origin O. In this distribution, a spherical cavity of radius $R_2$ , centred at $P$ with distance $\mathrm{OP}=a=R_1-R_2$ (see figure) is made. If the electric field inside the cavity at position $\vec r$ is $\vec E(\vec r)$ , then the correct statement(s) is(are)

A large shaded sphere of radius R₁ centred at O, with a small spherical cavity of radius R₂ centred at P, touching the outer surface from inside; the distance OP = a is shown dashed.

\vec E

is uniform, its magnitude is independent of

R_2

but its direction depends on

\vec r

\vec E

is uniform, its magnitude depends on

R_2

and its direction depends on

\vec r

\vec E

is uniform, its magnitude is independent of

a

but its direction depends on

\vec a

\vec E

is uniform and both its magnitude and direction depend on

\vec a

Answer and worked solution

Official answer: D

Superposition. Treat the cavity as a full sphere of density $\rho$ plus a small sphere of density $-\rho$ centred at P. Inside the cavity,
$\vec E=\frac{\rho\vec r}{3\varepsilon_0}-\frac{\rho(\vec r-\vec a)}{3\varepsilon_0}=\frac{\rho\vec a}{3\varepsilon_0}.$

The field is uniform, and both its magnitude and its direction depend on $\vec a$ .

(D)

Topics:Electric flux and Gauss's law Electric field

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JEE Advanced 2015 · Paper 2, Physics question 11