Please see the attached file:
3. Consider the case of an infinite conducting cylinder of radius 'a' with a uniform charge per unit length lambda placed in a uniform electric field with the axis of the cylinder perpendicular to the direction of the field. The potential generated by such a system maybe written as: (See attachment for equation)
a. calculate the electric field in the region outside the cylinder
b. calculate the charge distribution induced on the surface of the cylinder
c. calculate the force per unit length experienced by the cylinder
This entry considers an important question of a conducting cylinder placed in an external uniform electric field.
Electric field induced in the whole space is calculated, as well as the charge density on the surface of the cylinder and forces acting on the cylinder. Basic principles of electrostatics of conductors are nicely illustrated in this
example. Technical details of calculations are provided.