Two concentric co - planar circular loops of radius R and `r (lt lt R)` are placed as shown in the figure. The mutual inductance of the system will be

Options

A. `(pi mu _(0) r ^(2))/( 2R)`
B. `( pi mu _(0) r ^(2))/( 4 R)`
C. `(pi mu _(0) R ^(2))/( 4 r )`
D. `( pi mu _(0) R ^(2))/( 2 r)`

Answer

A

Explanation

The magnetic flux through the smaller loop due to the bigger loop is
`phi _(21) = (( mu _(i) )/( 2R)) xx pi r ^(2)`
`implies M = ( phi _(21))/( i) = (( pi mu _(0) r ^(2))/( 2 R))`