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  • Two straight and long conductors AOB and COD are perpendicular to each other and carry currents of I1 and I2. The magnitude of the magnetic field at a point P at a distan

Two straight and long conductors AOB and COD are perpendicular to each other and carry currents of I1 and I2. The magnitude of the magnetic field at a point P at a distance a from point O in a direction perpendicular to the plane ABCD is
 

Option: 1

\mathrm{\frac{\mu_0}{2 \pi a}\left(I_1+I_2\right) }


Option: 2

\mathrm{\frac{\mu_0}{2 \pi a}\left(I_1-I_2\right) }


Option: 3

\mathrm{\frac{\mu_0}{2 \pi a}\left(I_1^2+I_2^2\right)^{1 / 2} }


Option: 4

\mathrm{\frac{\mu_0}{2 \pi a} \frac{I_1 I_2}{\left(I_1+I_2\right)}}


Answers (1)

best_answer

The magnetic field at point P due to current \mathrm{I_1}  in conductor AOB is

\mathrm{B_1=\frac{\mu_0 I_1}{2 \pi a}}
and the magnetic field at point P due to current \mathrm{I_2}  in conductor COD is

\mathrm{B_2=\frac{\mu_0 I_2}{2 \pi a}}
Since the two conductors are perpendicular to each other, fields \mathrm{B_1}   and \mathrm{B_2} will be perpendicular to each other. Therefore, the resultant field at P is
\mathrm{ B=\left(B_1^2+B_2^2\right)^{1 / 2}=\frac{\mu_0}{2 \pi a}\left(I_1^2+I_2^2\right)^{1 / 2} }
Hence the correct choice is (c).

Posted by

vishal kumar

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