Magnetic Effects Of Current Question 26
Question: An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current of i ampere and the radius of the circular loop is r metre. Then the magnetic induction at its centre will be [MP PMT 1999]
Options:
A) $ \frac{{\mu_{0}}}{4\pi }\frac{2i}{r}(\pi +1) $
B) $ \frac{{\mu_{0}}}{4\pi }\frac{2i}{r}(\pi -1) $
C) Zero
D) Infinite
Show Answer
Answer:
Correct Answer: B
Solution:
The given shape is equivalent to the following diagram The field at $ O $ due to straight part of conductor is $ B_{1}=\frac{{\mu_{o}}}{4\pi }.\frac{2i}{r} $ ¤. The field at $ O $ due to circular coil is $ B_{2}=\frac{{\mu_{0}}}{4\pi }.\frac{2\pi i}{r}\otimes $ . Both fields will act in the opposite direction, hence the total field at O. i.e. $ B=B_{2}-B_{1}=( \frac{{\mu_{o}}}{4\pi } )\times (\pi -1)\frac{2i}{r}=\frac{{\mu_{o}}}{4\pi }.\frac{2i}{r}(\pi -1) $
BETA
