Electric Field Strength of a Uniformly Charged Cylinder

Electric field strength refers to the force per unit charge experienced by a test charge placed in an electric field. In the case of a uniformly charged cylinder, the electric field strength both inside and outside the cylinder is determined by the distribution of charges along with the distance from the center of the cylinder.

Outside the Cylinder (r ≥ R):

When considering points outside the cylinder with a distance r greater than the radius R, the electric field is determined by using a Gaussian surface that is a cylindrical shell co-axial to the charged cylinder. The electric field strength at these points is given by the formula: E = (λ/2πε₀)r , where λ represents the linear charge density and ε₀ is the permittivity of free space.

Inside the Cylinder (r ≤ R):

For points inside the cylinder with a distance r less than or equal to the radius R, the Gaussian surface used is a cylinder co-axial with the charged cylinder but with a radius r. The electric field inside the cylinder varies and is determined by the charge distribution within the cylinder.

When the distance r is equal to the radius R, the electric field strength inside and outside the cylinder should match. By substituting r=R in the equations for electric field strength outside and inside the cylinder, we can observe that they indeed equal at the boundary, confirming the continuity of the electric field across the surface of the cylinder.