# Electric charges and field Part – 13

Force per unit area of a charged conductor:

Let us consider the electric field E at any point P very near, but outside, the surface of a charged conductor is E = E1 + E2. Where E1 is the field due to the charge of small area ds around P, and E2 due to the charge on the rest of the surface.

Consider a point Pâ€™ opposite to P near the surface, but inside the conductor. For the point Pâ€™ the electric field E = E1 – E2 = 0.

So, E1 = E2 = . The electric field near the surface of a charged conductor is E = . Where Â is the surface charge density.

The force acting on the charge ds due to the charges of rest of the surface is F = dsE2 = .

Force per unit area of a charged conductor is Â = Â = .

Dipole moment on a charged ring:

A nonconducting ring of mass m radius r is vertically rest on a smooth non conducting horizontal plane. Charges +q and -q is distributed uniformly on the ring. Let dq is the charge at an angle for elementary part dl of the ring. So, dq = Î»rdÎ¸. The dipole moment for dq on both side of the ring is dP = dq2r cos = Î»rdÎ¸2r cos = 2Î»r2 cos dÎ¸.

The net dipole moment for the entire ring is

P = Â = 2Î»r2 cos d Â = 2Î»r2[sin Â = 4Î»r2 =4r2( ) = .

The torque acting on the ring in electric field:

A nonconducting ring of radius r is vertically rest on a smooth non conducting horizontal plane. Charges +q and -q is distributed uniformly on th part of the ring as shown in figure. A uniform electric field E is set up parallel to the horizontal plane. Let dq is the charge at an angle Â for elementary part dl of the ring.

So, dq = Î»rdÎ¸. Force acting on dq is dF = dqE = Î»rdÎ¸E.

The torque due to E is d = dF2r sin = 2Î»r2E sin dÎ¸

The torque acting on the ring is Â = = 2Î»r2E sin d Â = 2Î»r2E = 2Er2( ) = .

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