Magnetic Effects Of Current Question 430
Question: A thin rod is bent in the shape of a small circle of radius r. If the charge per unit length of the rod is a, and if the circle is rotated about its axis at a rate of n rotations per second, the magnetic induction at a point on the axis at a large distance y from the centre
Options:
A) $ {\mu_{0}}\pi r^{3}n\frac{\sigma }{y^{3}} $
B) $ 2{\mu_{0}}\pi r^{3}n\frac{\sigma }{y^{3}} $
C) $ ( \frac{{\mu_{0}}}{4\pi } )r^{3}n\frac{\sigma }{y^{3}} $
D) $ ( \frac{{\mu_{0}}}{2\pi } )r^{3}n\frac{\sigma }{y^{3}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Current, $ I=\frac{2\pi r\sigma }{\ell /n}=2\pi r\sigma n $ . $ B=\frac{{\mu_{0}}Ir^{2}}{2{{(y^{2}+r^{2})}^{3/2}}}=\frac{{\mu_{0}}Ir^{2}}{2y^{3}} $ If $ y»r $ . $ B=\frac{{\mu_{0}}r^{2}}{2y^{2}}(2\pi r\sigma n)=\frac{{\mu_{0}}\pi r^{3}\sigma n}{y^{3}} $
BETA
