Magnetic Effects Of Current Question 54
Question: A straight wire of length $ ({{\pi }^{2}}) $ metre is carrying a current of 2A and the magnetic field due to it is measured at a point distant 1 cm from it. If the wire is to be bent into a circle and is to carry the same current as before, the ratio of the magnetic field at its centre to that obtained in the first case would be [Haryana CEE 1996]
Options:
A) 50 : 1
B) 1 : 50
C) 100 : 1
D) 1 : 100
Show Answer
Answer:
Correct Answer: B
Solution:
If a wire of length l is bent in the form of a circle of radius r then $ 2\pi r=l $
Þ $ r=\frac{l}{2\pi } $ $ \vec{F}=i(\vec{L}\times \vec{B}) $ Magnetic field due to straight wire $ B_{1}=\frac{{\mu_{0}}}{4\pi }\cdot \frac{2i}{r}=\frac{{\mu_{0}}}{4\pi }\times \frac{2\times 2}{1\times {{10}^{-2}}} $ also magnetic field due to circular loop $ B_{2}=\frac{{\mu_{0}}}{4\pi }\cdot \frac{2\pi i}{r}=\frac{{\mu_{0}}}{4\pi }\cdot \frac{2\pi \times 2}{\pi /2} $
Þ $ \frac{B_{2}}{B_{1}}=\frac{1}{50} $
BETA
