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  4. A direct current I flows along the length of an infinitely long straight thin walled pipe, then the magnetic field

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Q. A direct current $I$ flows along the length of an infinitely long straight thin walled pipe, then the magnetic field

KCETKCET 2009Moving Charges and Magnetism

Solution:

Required arrangement is shown in figure. According to Ampere's circuital law.
image
For an internal point, $ r< R$
$B_{\text {internal }}=\frac{\mu_{0}(0)}{2 \pi r}=0$
For a point on the pipe, $r=R$
$B=\frac{\mu_{0} I}{2 \pi r}$
For an external point, $r < R$
$B_{\text {extemal }}=\frac{\mu_{0} I}{2 \pi r}$