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PHYS 225 Fall 2003

Selected Problems in Electricity and Magnetism

Mid-term exam 1

1. For a point charge q being at a distance (0, 0, d) above an infinite grounded conducting plane, can be






taken as if there being a negative Cq below the plane at a distance (0, 0, -d).

a.
Calculate the potential at any position (x, y, z) above

the conducting plane.





b.
Calculate the work required for preventing q from



infinity to d.



(Coulomb law, with r being the distance between the two charges)



c.
Assuming that there is no conducting plane but a negative charge Cq being at the position of (0, 0, -d), what would be the work required for preventing q from infinity to have a distance of 2d to Cq.




(Hint: when calculating question b and c, pay attention to the expression of F and the limits of the integral. The answer of c is double of that for b.)

2. The general solution of the Laplaces equation in a spherical coordinate is



R

z

As shown in the figure, a sphere with radius R is in an otherwise uniform electric field E along z-direction. Calculate the field inside the sphere in the following two cases:

a.
The sphere is a metal one;




b.
The sphere is a dielectric one with homogeneous relative dielectric constant .




(Hint:









At r = R,



and