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PhysicsSingle correct+3 / -1Question 6 of 66

IIT-JEE 2007 · Paper 2, Physics question 6

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

A shaded solid sphere with a smaller spherical cavity inside it, off-centre (the cavity's centre is below the sphere's centre).
Choose one option
Answer and worked solution

Official answer: B

Superposition. Treat the cavity as the full sphere (charge density ρ) plus a small sphere of density −ρ-\rho. Inside a uniform ball the field is ρ3ε0r⃗\dfrac{\rho}{3\varepsilon_0}\vec r from its centre. At a point in the cavity:
E⃗=ρ3ε0r⃗1−ρ3ε0r⃗2=ρ3ε0(r⃗1−r⃗2)=ρ3ε0d⃗,\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}\vec d,
where d⃗\vec d joins the sphere's centre to the cavity's centre.

So the field in the cavity is the same everywhere and nonzero (the centres differ).

(B)

Topics:Electric fieldElectric flux and Gauss's law
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