Question

obtain an expression for the electric field intensity at a point outside an infinitely long charged cylindrical conductor​

Answer 1

Answer:

Consider an isolated infinitely long cylindrical conductor A, of radius R and carrying a charge per unit length (linear charge density) λ.

Consider a point P outside the conductor at a distance r from its axis. To find the electric field intensity at P, we choose a cylindrical Gaussian surface S of radius r through P and coaxial with conductor A. A small area element containing P has an area dS.

Charge is uniformly distributed over the outer surface of the conductor. Then, by symmetry, the electric field intensity at any point outside the conductor is at right angles to the cylinder axis. Hence, the component of the electric field intensity perpendicular to the plane circular faces of the Gaussian surface is zero. Therefore, the total normal electric induction (TNEI) through these flat faces is zero.

At every point on the curved face of surface S, by symmetry, the electric field intensity E→ is normal to S and has the same magnitude E. If the charge on conductor A is positive, E→ is directed along the outward drawn normal.ion: