(a) Write two important characteristics of equipotential surfaces.
(b) A thin circular ring of radius r is charged uniformly so that its linear charge density becomes λ. Derive an expression for the electric field at a point P at a distance x from it along the axis of the ring. Hence, prove that at large distance (x>>r), the ring behaves as a point charge.
OR
(a) State Gauss's law on electrostatics and derive an expression for the electric field due to a long straight thin uniformly charged wire (linear charge density λ) at a point lying at a distance r from the wire.
(b) The magnitude of electric field (in NC-1) in a region varies with the distance r (in m) as E = 10r + 5. By how much does the electric potential increases in moving from point at r = 1 m to a point at r = 10m.
[2020 | Delhi | Section - D | SET - 1 SET - 2 SET - 3, Q.37 Q.35 Q.36]
