Physics · Electrostatics
A neutral conducting sphere of radius R is placed in a uniform electric field of magnitude E0 pointing along the z-axis. The electrostatic potential at any point r (r > R) outside the sphere is given by V(r, θ) = V0 - E0r(1 - R3/r3)cos(θ), where V0 is the constant potential of the sphere. Which of the following statements is correct?
- 1The electric field at any point for r > R has a non-zero divergence
- 2The electric field at any point for r > R is not curl-free
- 3As r → ∞, the electric field is given by E = E0cos(θ) r̂
- 4The induced surface charge density on the sphere is proportional to cos(θ)✓
Correct answer
The induced surface charge density on the sphere is proportional to cos(θ)
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