A) \[3:4\]
B) \[3:5\]
C) \[2:3\]
D) \[4:3\]
Correct Answer: A
Solution :
For wire A Length \[=40\text{ }cm\] It is bent into a circle, so \[\therefore \] \[2\pi r=40\] \[r=\frac{40}{2\pi }\] Magnetic induction at centre \[=\frac{{{\mu }_{0}}{{i}_{1}}}{2r}\] For wire B Length =30 cm It is bent into an arc, so \[\therefore \]\[\theta \,r\,=30\] Magnetic induction at centre due to circular arc \[=\frac{{{\mu }_{0}}{{i}_{2}}\theta }{4\pi r}\] Since, \[\frac{{{\mu }_{0}}\,{{i}_{1}}}{2\,r}=\frac{{{\mu }_{0}}\,{{i}_{1}}\theta }{4\pi \,r}\] \[\Rightarrow \] \[\frac{{{i}_{1}}}{{{i}_{2}}}=\frac{\theta }{2\pi }=\frac{30\times 2\pi }{2\pi \times 40}\] \[\Rightarrow \] \[\frac{{{i}_{1}}}{{{i}_{2}}}=\frac{3}{4}\]
You need to login to perform this action.
You will be redirected in
3 sec
