Description
Problems
1. A strip with current:
A straight and infinitely long strip of width 2a carries a current I which is uniformly
distributed across the width of the strip. The strip is positioned in the x = 0 plane
between y = −a and y = a, the current is in the z direction.
(a) (25 pts) Find the magnetic field B~ at an arbitrary point ~r = (x, y, z).
(b) (10 pts) To check your result consider the limiting case of large distances from
the strip.
2. A rotating sphere:
A sphere of radius a carries a uniform surface-charge distribution σ. The sphere is
rotated about a diameter with constant angular velocity ω.
(a) (35 pts) Find the vector potential A~ and the magnetic field B~ inside and outside
the sphere.
3. Current flow over a sphere:
A current I starts at z = −∞ and flows up the z-axis as a linear filament until it hits
an origin-centered sphere of radius R. The current spreads uniformly over the surface
of the sphere and flows up lines of longitude from the south pole to the north pole.
The recombined current flows thereafter as a linear filament up the z-axis to z = +∞.
(a) (5 pts) Find the current density on the sphere.
(b) (20 pts) Use explicitly stated symmetry arguments and Ampere’s law in integral
form to find the magnetic field at every point in space.
(c) (5 pts) Check that your solution satisfies the magnetic field matching conditions
at the surface of the sphere.
