HW$15$: Magnetic Sources

Score: $\frac{3\mathrm{.}5}{8}$ Answered: $\frac{3}{6}$

MAGNETIC FIELD OF AN EXTENDED COIL

Consider a coil consisting of $48$ loops of wire that are wrapped around the outside of tube with a $13\mathrm{.}2$ cm diameter and a $3\mathrm{.}3$ cm length. The coil's loops are carefully wrapped so that they are uniformly distributed over the tube's length.

If the coil carries a $174$ mA current, what is the magnitude of the magnetic field at the center of the tube?

Hint: Write out the magnetic field $dB$ of a small loop within the coil and integrate to obtain the magnetic field of the entire coil.

$B=T$