Magnetic Effects Of Current Question 37
Question: The magnetic induction at the centre O in the figure shown is [IIT 1988; KCET 2002]
Options:
A) $ \frac{{\mu_{0}}i}{4}( \frac{1}{R_{1}}-\frac{1}{R_{2}} ) $
B) $ \frac{{\mu_{0}}i}{4}( \frac{1}{R_{1}}+\frac{1}{R_{2}} ) $
C) $ \frac{{\mu_{0}}i}{4}(R_{1}-R_{2}) $
D) $ \frac{{\mu_{0}}i}{4}(R_{1}+R_{2}) $
Show Answer
Answer:
Correct Answer: A
Solution:
In the following figure, magnetic fields at O due to sections 1, 2, 3 and 4 are considered as $ B_{1},,B_{2},,B_{3} $ and $ B_{4} $ respectively. $ B_{1}=B_{3}=0 $ $ B_{2}=\frac{{\mu_{0}}}{4\pi }.\frac{\pi ,i}{R_{1}}\otimes $ $ B_{4}=\frac{{\mu_{0}}}{4\pi }.\frac{\pi ,i}{R_{2}} $ ¤ As $ |B_{2}|>|B_{4}| $ So $ B_{net}=B_{2}-B_{4}\Rightarrow B_{net}=\frac{{\mu_{0}}i}{4}( \frac{1}{R_{1}}-\frac{1}{R_{2}} )\otimes $
BETA
