Magnetic Effects Of Current Question 421
Question: Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field $ B_{1} $ , at its centre when a current I passes through it. The ratio $ B_{1}:B_{2} $ is:
Options:
A) 1 : 1
B) 1 : 3
C) 1 : 9
D) 9 : 1
Show Answer
Answer:
Correct Answer: B
Solution:
[b] For loop $ B=\frac{{\mu_{0}}nI}{2a} $ where, a is the radius of loop. Then, $ B_{1}=\frac{{\mu_{0}}I}{2a} $ Now, for coil $ B=\frac{{\mu_{0}}I}{4\pi }.\frac{2n,A}{x^{3}} $ at the centre x = radius of loop $ B_{2}=\frac{{\mu_{0}}}{4\pi }.\frac{2\times 3\times (I/3)\times \pi {{(a/3)}^{2}}}{{{(a/3)}^{3}}}=\frac{{\mu_{0}}.3I}{2a} $
$ \therefore \frac{B_{1}}{B_{2}}=\frac{{\mu_{0}}I/2a}{{\mu_{0}}.3I/2a} $ $ B_{1}:B_{2}=1:3 $
BETA
