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Two non-conducting spheres of radii R1 a...

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

A

the electrostatic field is zero

B

the electrostatic potential is constant

C

the electrostatic field is constant in magnitude

D

the electrostatic field has same direction.

Text Solution

Verified by Experts

In triangle `PC_(1)C_(2), vec(r)_(2)=vec(d) +vec(r)_(1)`
The electrostatic field at point P is
`vec(E)=(K(rho 4/3pi R_(1)^(3))vec(r)_(2))/(R_(1)^(3))+(K(rho4/3 piR_(2)^(3))(vec(r)_(1))/(R_(2)^(3))`
`=K rho 4/3 pi(vec(r)_(2)-vec(r)_(1))=(rho)/(3epsilon_(0)) vec(d)`
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