Magnetic Effects Of Current Question 131
Question: A circular current carrying coil has a radius R. The distance from the centre of the coil on the axis where the magnetic induction will be $ \frac{1}{8}th $ to its value at the centre of the coil, is [MP PMT 1997]
Options:
A) $ \frac{R}{\sqrt{3}} $
B) $ R\sqrt{3} $
C) $ 2\sqrt{3},R $
D) $ \frac{2}{\sqrt{3}}R $
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Answer:
Correct Answer: B
Solution:
$ \frac{B_{centre}}{B_{axis}}={{( 1+\frac{x^{2}}{R^{2}} )}^{3/2}}, $ also $ B_{axis}=\frac{1}{8}B_{centre} $
$ \Rightarrow \frac{8}{1}={{( 1+\frac{x^{2}}{R^{2}} )}^{3/2}}\Rightarrow 2={{( 1+\frac{x^{2}}{R^{2}} )}^{1/2}} $
$ \Rightarrow 4=1+\frac{x^{2}}{R^{2}}\Rightarrow 3=\frac{x^{2}}{R^{2}}\Rightarrow x^{2}=3R^{2} $
$ \Rightarrow x=\sqrt{3}R $
BETA
