Consider a uniform spherical charge distribution of radius R1 centred at the origin O. In this distribution, a spherical cavity of radius R2, centred at P with distance OP=a=R1−R2 (see figure) is made. If the electric field inside the cavity at position r→ is E→r→, then the correct statement(s) is (are)
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a
E→ is uniform, its magnitude is independent of R2 but its direction depends on r→
b
E→ is uniform, its magnitude depends on R2 and its direction depends on r→
c
E→ is uniform, its magnitude is independent of a but its direction depends on a→
d
E→ is uniform and both its magnitude and direction depend on a→
answer is D.
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Detailed Solution
The sphere with cavity can be assumed as a complete sphere with +ve charge, radius R1 + another complete sphere with –ve charge, radius R2 .Inside a spherical charge distribution for an internal point E→=ρ3ε0r→ E+→E due to total +ve charges E−→E due to total −ve charges Electric filed at any point inside cavity is given by,E→ =E→ ++E→ − ⇒E→=ρ3ε0r1→+-ρ3ε0r2→=ρ3ε0r1→-r2→=ρ3ε0a→ E→ is uniform and both its magnitude and direction depend on a→