Question
Show that the magnitude of the magnetic field produced at the center of a rectangular loop of wire of length $L$ and width $W$carrying a current $i,$ is$$B=\frac{2 \mu_{0} i}{\pi} \frac{\left(L^{2}+W^{2}\right)^{1 / 2}}{L W}$$
Step 1
We can use the Pythagorean theorem to find the hypotenuse of the right triangle formed by half the length and half the width of the rectangle. This gives us: $$ r = \sqrt{\left(\frac{L}{2}\right)^2 + \left(\frac{W}{2}\right)^2} = \frac{\sqrt{L^2 + W^2}}{2} $$ Show more…
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Show that the magnitude of the magnetic field produced at the center of a rectangular loop of wire of length $L$ and width $W$ carrying a current $i,$ is $$ B=\frac{2 \mu_{0} i}{\pi} \frac{\left(L^{2}+W^{2}\right)^{1 / 2}}{L W} $$
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