JEE Advanced 2013 · Paper 2 · Physics Q2

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PhysicsMultiple correct+3 / -1Question 2 of 60

Two non-conducting spheres of radii $R_1$ and $R_2$ and carrying uniform volume charge densities $+\rho$ and $-\rho$ , respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region,

Two overlapping spheres: the left one of radius R₁ with charge density +ρ and the right one of radius R₂ with −ρ; the lens-shaped overlap is hatched.

the electrostatic field is zero.

the electrostatic potential is constant.

the electrostatic field is constant in magnitude.

the electrostatic field has same direction.

Answer and worked solution

Official answer: C, D

Superposition. Inside a uniform ball the field is $\dfrac{\rho}{3\varepsilon_0}\vec r$ from its centre. In the overlap,
$\vec E=\frac{\rho}{3\varepsilon_0}\vec r_1-\frac{\rho}{3\varepsilon_0}\vec r_2=\frac{\rho}{3\varepsilon_0}\left(\vec r_1-\vec r_2\right)=\frac{\rho}{3\varepsilon_0}\overrightarrow{C_1C_2},$
a uniform field: constant magnitude and the same direction everywhere, so the potential varies along it.

(C), (D)

Topics:Electric field Electric flux and Gauss's law

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JEE Advanced 2013 · Paper 2, Physics question 2