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(PHYS225)PHYS225-03-mid-term-2.pdf
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PHYS 225 Fall 2003

Selected Problems in Electricity and Magnetism

Mid-term exam 2

1. If an electron moving along x direction facing an electric field along y direction,
and a magnetic field along z direction,
, if the speed of the electron is
, what is the total force (in unit of N) applied to the electron?

Hint: electron charge



2. A steady current I flows down a long cylindrical wire of radius a (see the figure), find the magnetic field both inside and outside the wire, if

a.
The current is uniformly distributed only over the thin surface shell of the wire;




b.
The current is distributed in such a way that the current density (current per unit area) J is proportional to s, the distance from the axis.






Hint:


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


a.
The sphere is a metal one;



b.
The sphere is a dielectric one with homogeneous

relative dielectric constant .



Hints for question b:









At r = R,
and


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: