Problem :
A wire carrying a current I runs from the origin to the point (0, d ) , shown below. What is the strength of the magnetic field at the point (r, 0) ?
Recall that when we derived the field of an infinite straight wire we evaluated an integral from negative infinity to infinity. We are still dealing with a straight wire here; we must simply change our limits of integration. Recall that:
for an infinite wire. For our wire, we simply integrate from 0 to d :
B | = | ||
= | - | ||
= | - |
Problem :
What is the magnitude and direction of the magnetic field at the center of a square wire with sides of length d and current I ?
We begin by drawing a diagram:
B | = | ||
= | + | ||
= | |||
= | = |
Again, the direction of the field is out of the page.