Question

A short solenoid of length $ 4\, cm $ , radius $ 2 \,cm $ and $ 100 $ turns is placed inside and on the axis of a long solenoid of length $ 80 \,cm $ and $ 1500 $ turns. A current of $ 3\, A $ flows through the short solenoid. The mutual inductance of two solenoids is:

• A. $ 2.96\times {{10}^{-4}}H $
• B. $ 5.3\times {{10}^{-5}}H $
• C. $ 3.52\times {{10}^{-3}}H $
• D. $ 8.3\times {{10}^{-5}}H $
• E. $ 2.96\times {{10}^{-3}}H $

Answer 1

Answer: (A)

$ {{M}_{21}}=\frac{{{\mu }_{0}}{{N}_{1}}{{N}_{2}}{{A}_{2}}}{{{l}_{1}}} $
$ \therefore $ $ {{M}_{21}}=\frac{\begin{align} & (4\times 3.14\times {{10}^{-7}})\times 1500\times 100 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\times \{3.14{{(2\times {{10}^{-2}})}^{2}}\} \\ \end{align}}{80\times {{10}^{-2}}} $
$ {{M}_{21}}=2.96\times {{10}^{-4}}H $
$ \Rightarrow $ $ {{M}_{21}}={{M}_{21}}=2.96\times {{10}^{-4}}H $