Magnetic Effects Of Current Question 420
Question: A wire carries a current. Maintaining the same current it is bent first to form a circular plane coil of one turn which produces a magnetic field B at the centre of the coil. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the centre of the double loop, caused by the same current is
Options:
A) $ 4B $
B) $ B/4 $
C) $ ~B/2 $
D) $ 2B $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Let $ I $ be current and I be the length of the wire. For 1st case: $ B=\frac{{\mu_{0}}In}{2r}=\frac{{\mu_{0}}I\times \pi }{l} $ where $ 2\pi r=l $ and n = 1 For $ II,nd $ Case: $ l=2(2\pi r’)\Rightarrow r’=\frac{l}{4\pi } $ $ B’=\frac{{\mu_{0}}nI}{2r’}=\frac{{\mu_{0}}2I}{2\frac{l}{4\pi }}=\frac{4{\mu_{0}}I\pi }{l}=4B $
BETA
