Magnetic Effects Of Current Question 135
Question: A cell is connected between the points A and C of a circular conductor ABCD of centre O with angle A $ OC=60^{o} $ . If $ B_{1} $ and $ B_{2} $ are the magnitudes of the magnetic fields at O due to the currents in ABC and ADC respectively, the ratio $ \frac{B_{1}}{B_{2}} $ is [KCET 1999; Pb PET 2000]
Options:
A) 0.2
B) 6
C) 1
D) 5
Show Answer
Answer:
Correct Answer: C
Solution:
$ B=\frac{{\mu_{0}}}{4\pi }\frac{\theta ,i}{r}\Rightarrow B\propto \theta ,i $ (but $ \frac{i_{1}}{i_{2}}=\frac{l_{2}}{l_{1}}=\frac{{\theta_{2}}}{{\theta_{1}}} $ )
$ \Rightarrow \frac{B_{1}}{B_{2}}=\frac{{\theta_{1}}}{{\theta_{2}}}.\frac{i_{1}}{i_{2}} $ So, $ \frac{B_{1}}{B_{2}}=\frac{{\theta_{1}}}{{\theta_{2}}}\times \frac{{\theta_{2}}}{{\theta_{1}}} $
$ \Rightarrow B_{1}=B_{2} $
BETA
