Class Problem 19
1. A small line segment 2.0mm long carries a 5.0A current in the x-direction. Find the magnitude of the
magnetic field and the angle between the magnetic field and the z-axis at the points (3,0,0) and (1,2,3)
where the coordinates are in meters.
2. Find the magnetic field at the center of a closed current loop consisting of two semicircular arcs as
shown. The radii are 40cm and 20 cm, and the current is 5.0A.
3. The earth’s magnetic field at the north pole is 0.600G pointing straight down. Assuming it is created by
a ring current running at the equator, how large and in what direction would that current be? (Radius of
the earth = 6,400 km)
4. A 50-turn coil of radius 10.0cm carries a current of 4.00A and a concentric 20-turn coil of radius 0.500
cm carries a current of 1.00A. The planes of the two coils are perpendicular to each other. Find the
magnitude of the torque exerted by the large coil on the small coil. (Neglecting any variation of the
magnetic field due to the large coil in the region of the small coil.)
5. A pair of Helmholtz coils that have radii R have their axes along the z axis. One coil is in the z   R 2
plane and other on the z  R 2 plane. The coils carry equal current I running parallel to each other. Find
the magnetic field at the point (0,0,z). Show that at z=0, the derivatives
dBz dz, d 2 Bz dz 2 , d 3 Bz dz 3 are all equal to zero. (so that the magnetic field is fairly uniform near
the center)