## PHYS208 Fundamentals of Physics II

### Quiz 7 -- Current Distributions

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.

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

- What is the direction of the contribution to the field
*d***B** contributed by the infinitesimal current segment *d***s**_{1}
shown at the top of the loop?
Show it on the sketch.

- Consider the conjugate element
*d***s**_{2} at the bottom of the loop.
Present a sketch or brief discussion that demonstrates that the
total field **B** at point *P* is horizontal.

- Express the horizontal component of
*d***B** in terms of *x* and *a*.

- What is the total field strength
**B** at point *P*?

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

"http://www.physics.udel.edu/~watson/phys208/quiz7.html"

Last updated April 17, 1998.

Copyright George Watson, Univ. of Delaware, 1998.