Physics 2420 In-Class Problems:
Electric Fields from Charge Distributions

1. Find the electric field at a point a distance a from one end of a long thin wire of length L.
   (a) if it has total charge Q. Examine the limit a >> L and show that your result is identical to that of a point charge.
   (b) if the charge distribution was λ(x) = 2Qx/L².

   

2. Find the electric field at a point a distance a from the centre of a long thin wire of length L and total charge Q. Show that your result reduces to that of a point charge in the limit a >> L. Also show that your answer reduces to E = 2kλ/a in the limit L >> a, the well-known and very useful result for a long thin wire. Note λ = Q/L.

   

3. A wire has been bent into a semicircle of radius R. It has a linear charge density λ. Determine the electric field at point P, at the centre of the circle.

   

4. Find the electric field at a point a distance h from the centre of a circular plate of radius R with charge Q. Show that your answer reduces to that of a point charge in the limit h >> R (the point is very far away from the plate). Show that your answer reduces to the well-known result E = Σ/2e ₀ when R >> h (the plate is infinite or the point is very close to the plate). Note Σ = Q/A.

   

5. A hollow sphere of radius R has a surface charge s . Find the electric field at a point along the z axis outside the sphere. Find the electric field at a point along the z axis inside the sphere.

6. A hollow half cylinder is shown below has surface charge s . The cylinder has height L and radius R. The back of the hollow cylinder is a flat rectangle. Derive the integrals necessary to find the electric field outside the cylinder on the y axis a distance d from the back of the half cylinder. There is no need to solve the integrals.

   

7. The solid half-cylinder shown above has charge density r . It has height L and radius R. Derive the integrals necessary to find the electric field at a point outside the cylinder on the y axis. There is no need to solve the integral.

Questions? mike.coombes@kwantlen.ca