What is the point of maximum magnetic field on the axis of a ring wire?
The equation for magnetic field on the axis of a ring is:
Two rings of radius 1 cm and parallel current I are placed a distance of 2 cm apart, as shown below. What is the magnitude of the magnetic field at the point on their common axis midway between the two rings?
The contribution of both rings to the magnetic field is in the positive direction and, since the point is equidistant from both rings, both contribute the same magnitude of magnetic field. Thus we simply need to calculate the contribution by one ring, and double it. The contribution by one ring is given by:
A semi-infinite solenoid is a solenoid which starts at a point, and is infinite in length in one direction. What is the strength of the magnetic field on the axis of the solenoid at the end of a semi-infinite solenoid?
To solve this problem, we use the superposition principle. If we put two semi- infinite solenoids end to end, we have an infinite solenoid, and the field strength at any point in the infinite solenoid is . By symmetry, the contribution of each semi-infinite solenoid is equal, so the contribution of one semi-infinite solenoid must be exactly one half of the magnetic field in an infinite solenoid, or
Two rings, both with radius b, with a common center and the same current I are placed at right angles to each other, as shown below. What is the magnitude and direction of the magnetic field at their center?
Each ring contributes the same magnitude of magnetic field, though in perpendicular directions, as shown below. The magnitude of each vector is simply: