Charge related physics question

Question

A +ve charge (+q) is kept in the vacinity of an uncharged conducting plate. Sketch electric field lines originating from the point on to the surface of the plate.Derive the expression for the electric field at the surface of charged conductor.

Answer 1

It looks like you have 2 different problems here.  The first one calls for a sketch, which this forum is not set up for.  I will solve the second problem:

 

"Derive the expression for the electric field at the surface of charged conductor."

 

Have you seen Gauss' law in your physics class?  I will use it below, for a charged surface of infinite extent.

 

Apply Gauss' law.  For the Gaussian surface, consider a cylinder intersected by the charged plane at the middle, splitting the cylinder into 2 equal cylinders, one above the charged surface and one below the charged surface.  Let σ be the surface charge density, and let A be the cross sectional area of the 2 cylinders.  The interior charge of the undivided cylinder is σA.  By the symmetry of this configuration, the electric field lines must be normal to the circular surfaces at the ends of the undivided cylinder, with no electric field lines crossing the cylindrical surface that is parallel to the axis.  Then by Gauss' law, the electric flux Φ is

 

Φ = σA/ε₀

 

By the symmetry of this configuration, 

 

Φ = AE + AE = 2AE ⇒

 

2AE = σA/ε₀

 

E = σ/(2ε₀)

 

Note the answer does not depend on the distance from the charged surface.