PHYS208 Fundamentals of Physics II

Quiz 7 -- Current Distributions

Field lines of circular current ring

Evaluate the magnetic field B on the axis of a circular current loop at point P, a distance x from the center of the loop having radius a.

The magnetic field lines are shown at right. There is not enough symmetry in this situation to invoke Ampere’s law easily for the calculation of the field.

  1. What is the formula for the Biot-Savart law?

    Circular current ring

  2. What is the direction of the contribution to the field dB contributed by the infinitesimal current segment ds1 shown at the top of the loop? Show it on the sketch.

  3. Consider the conjugate element ds2 at the bottom of the loop. Present a sketch or brief discussion that demonstrates that the total field B at point P is horizontal.

  4. Express the horizontal component of dB in terms of x and a.

  5. What is the total field strength B at point P?

  6. Check the limit of the above expression for x = 0, the point at the center of the loop.

Last updated April 17, 1998.
Copyright George Watson, Univ. of Delaware, 1998.