Question

Two concentric circular coils, one of radius $2cm$ and the other of radius $4m$, are placed co-axially with centres coinciding.The mutual inductance of the arrangement is:-

• A. $5{\mu }_0\pi \times {10}^{-3}H$
• B. $5{\mu }_0\pi \times {10}^{-5}H$
• C. $5{\mu }_0\times {10}^{-5}H$
• D. $5{\mu }_0\pi \times {10}^{-4}H$

Answer 1

The correct option is C $5{\mu }_0\times {10}^{-5}H$

$\begin{array}{c}\varphi =\frac{{\mu }_{o}i}{2\left(4\right)}\left(\frac{\pi {\left(2\right)}^2}{10000}\right)\\ =\frac{{\mu }_{o}i\pi \times {10}^{-4}}{2}\\ =\left(\frac{{\mu }_o\pi \times {10}^{-4}}{2}\right)i\\ \therefore M=\frac{10\times {\mu }_o\pi \times {10}^{-5}}{2}\\ =5{\mu }_o\pi \times {10}^{-5}H\\ Hence,\\ optionCiscorrectanswer.\end{array}$