Magnetic Effects Of Current Question 89
Question: Magnetic fields at two points on the axis of a circular coil at a distance of 0.05m and 0.2m from the centre are in the ratio 8 : 1. The radius of the coil is [KCET 2002]
Options:
A) 1.0 m
B) 0.1 m
C) 0.15 m
D) 0.2 m
Show Answer
Answer:
Correct Answer: B
Solution:
$ B=\frac{{\mu_{0}}}{4\pi }\times \frac{2\pi NiR^{2}}{{{(R^{2}+x^{2})}^{3/2}}}\Rightarrow B\propto \frac{1}{{{(r^{2}+x^{2})}^{3/2}}} $
$ \Rightarrow \frac{8}{1}=\frac{{{(R^{2}+x_{2}^{2})}^{3/2}}}{{{(R^{2}+x_{1}^{2})}^{3/2}}}\Rightarrow {{( \frac{8}{1} )}^{2/3}}=\frac{R^{2}+0.04}{R^{2}+0.0025} $
$ \Rightarrow \frac{4}{1}=\frac{R^{2}+0.04}{R^{2}+0.0025} $ . On solving $ R=0.1m $
BETA
