Magnetic Effects Of Current Question 134
Question: Two straight long conductors AOB and COD are perpendicular to each other and carry currents $ i_{1} $ and $ i_{2} $ . The magnitude of the magnetic induction at a point P at a distance a from the point O in a direction perpendicular to the plane ACBD is [MP PMT 1994]
Options:
A) $ \frac{{\mu_{0}}}{2\pi a}(i_{1}+i_{2}) $
B) $ \frac{{\mu_{0}}}{2\pi a}(i_{1}-i_{2}) $
C) $ \frac{{\mu_{0}}}{2\pi a}{{(I_{1}^{2}+I_{2}^{2})}^{1/2}} $
D) $ \frac{{\mu_{0}}}{2\pi a}\frac{I_{1}I_{2}}{(I_{1}+I_{2})} $
Show Answer
Answer:
Correct Answer: C
Solution:
At P : $ B_{net}=\sqrt{B_{1}^{2}+B_{2}^{2}} $ $ =\sqrt{{{( \frac{{\mu_{0}}}{4\pi }\frac{2i_{1}}{a} )}^{2}}+{{( \frac{{\mu_{0}}}{4\pi }\frac{2i_{2}}{a} )}^{2}}} $ $ =\frac{{\mu_{0}}}{2\pi a}{{(i_{1}^{2}+i_{2}^{2})}^{1/2}} $
BETA
