Magnetic field from loop current
The above left diagram shows a circular current with radius
and current intensity
flowing in the direction of the arrows. The above right diagram shows two concentric circular currents with radii
and
respectively, and the same current intensity
flowing in the direction of their respective arrows. Points
P
and
Q
are the centers of their respective circular currents. If the magnetic field intensity at point
P
is
then what is the magnetic field intensity at point
Q
?
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1 solution
Use Biot-Savart law twice. For the first case, evaluation of the equation for the law yields a value for B in terms of the electric constant, I and r (provided the differential length element is parameterized in terms of r and theta). For the second case (point Q), the value for B will be the same equation applied to the new current minus the current obtained for the first case. The second magnetic field comes out to B divided by two, subtracting the magnitude of the first field gives the value originally obtained for B. If someone could give me a link to a site describing how to use LaTex code I'd appreciate it.