Question

2. Figure shows a ring of radius R 4m and a point particle located at the center of the ring. Point P is on the central z axis, at distance z 3 m above the ring. The ring is charged with the uniform linear charge density of 1 10 C/m. What is the charge of the point particle, Q, if the net electrical field at point P is zero? -3 m R-4 m

Answer 1

Here, since, the net field is zero, we have to equate the two fields viz. The filed due to point charge, and the field due to the uniformly charged ring.

Note than both the fields are directed along the z direction.

In order to cancel the filed due to ring along , say, positive z axis, the charge must have equal field along negative z axis, and hence the charge must me negative.

Here, since, the net field is zero, we have to equate the two fields viz. The filed due to point charge, and the field due to the uniformly charged ring. Note than both the fields are directed along the z direction. In order to cancel the filed due to ring along, say, positive z axis, the charge must have equal field along negative z axis, and hence the charge must me negative. Electric filed due to a ring a point along its axis at a distance z is E_ring = k lambda 2 pi R z/(z62 + r62)^3/2 - (1) k = 1/4 pi epsilon_0 Electric filed due to a point charge is E_point = k Q/z62 - (2) if the net electric filed is zero E_ring + E_point = 0 from (1) and (2) k lambda 2 pi R z/(z62 + r^2)^3/2 = -k Q/z62 Therefore Q = -2 pi R lambda z^3/(z^2 + R^2)^3/2 - (3) here lambda = 1 times 10^-9 c/m