Magnetic Effects Of Current Question 236
Question: Two wires AO and OC carry equal currents i as shown in figure. One end of both the wires extends to infinity. Angle AOC is $ \alpha $ . The magnitude of magnetic field at point P on the bisector of these two wires at a distance r from point O is
Options:
A) $ \frac{{\mu_{0}}}{2\pi }\frac{i}{r}\cot ( \frac{\alpha }{2} ) $
B) $ \frac{{\mu_{0}}}{4\pi }\frac{i}{r}\cot ( \frac{\alpha }{2} ) $
C) $ \frac{{\mu_{0}}}{4\pi }\frac{i}{r}\frac{( 1+\cos \frac{\alpha }{2} )}{\sin ( \frac{\alpha }{2} )} $
D) $ \frac{{\mu_{0}}}{4\pi }\frac{i}{r}( \frac{\alpha }{2} ) $
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Answer:
Correct Answer: C
Solution:
[c] $ x=r\sin \frac{\alpha }{2} $
$ \therefore B_{p}=2( \frac{{\mu_{0}}}{4\mu } )( \frac{i}{x} )[ \sin ( 90{}^\circ -\frac{\alpha }{2} )+\sin 90{}^\circ ] $ $ =\frac{{\mu_{0}}}{2\pi }\frac{i}{r}\frac{( 1+\cos \frac{\alpha }{2} )}{\sin \frac{\alpha }{2}} $
BETA
