Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current I 1 and COD carries a current I 2 . The magnetic field on a point lying at

Question

Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current I 1 and COD carries a current I 2 . The magnetic field on a point lying at a distance of from O , in a direction perpendicular to the plane of the wires AOB and COD , will be given by

TestHub · Accepted Answer

The magnetic field inductions at a point $P_{1}$ at a distance d from O in a direction perpendicular to the plane of the wires due to the plane of the wires due to currents through AOB and COD are perpendicular to each other is

Hence, $B = \sqrt{B_{1}^{2} + B_{2}^{2}}$

$= {[{(\frac{μ_{0}}{4 π} \frac{2 I_{1}}{d})}^{2} + {(\frac{μ_{0}}{4 π} \frac{2 I_{2}}{d})}^{2}]}^{\frac{1}{2}}$

$= \frac{μ_{0}}{2 π d} \sqrt{(l_{1}^{2} + l_{2}^{2})}$

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