Magnetic field due to currentMedium
Question
Two identical circular loops P and Q each of radius $r$ are lying in parallel planes such that they have common axis. The current through P and Q are I and 4I respectively in clockwise direction as seen from O . The net magnetic field at O is:
Options
A.$\frac{3\mu_{o}I}{4\sqrt{2r}}$ toward P
B.$\frac{\mu_{o}I}{4\sqrt{2}r}$ toward P
C.$\frac{\mu_{o}I}{4\sqrt{2}r}$ towards Q
D.$\frac{3\mu_{0}I}{4\sqrt{2}r}$ towards $Q$
Solution
$B_{net} = B_{1} - B_{2}$
$${= \frac{4\mu_{0}iR^{2}}{2\left( R^{2} + R^{2} \right)^{3/2}} - \frac{\mu_{0}iR^{2}}{2\left( R^{2} + R^{2} \right)^{3/2}} }{= \frac{3\mu_{0}i}{4\sqrt{2}R}}$$
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