Question

An arrangement with a pair of quarter circular coils of radii r and R with a common centre C and carrying a current I is shown.
The permeability of free space is ${\mu }_0$. The magnetic field at C is :

• A. ${\mu }_{0}I(1/r-1/R)/8$ into the page.
• B. ${\mu }_{0}I(1/r-1/R)/8$ out the page.
• C. ${\mu }_0(1/r+1/R)/8$ into the page.
• D. ${\mu }_0(1/r+1/R)/8$ out the page.

Answer 1

The correct option is B ${\mu }_{0}I(1/r-1/R)/8$ out the page.

Magnetic field due to straight wire is 0,

B due to r radius wire $B_r=\frac{{\mu }_{o}I}{4\pi r}\times \frac{\pi }{2}$, out the Page

B due to R radius wire $B_R=\frac{{\mu }_{o}I}{4\pi R}\times \frac{\pi }{2}$,into the page

net $B_r-B_R=\frac{{\mu }_{o}I}{8}(\frac{1}{r}-\frac{1}{R})$ out the page