A) \[{{M}_{12}}={{M}_{21}}\]
B) \[{{M}_{12}}=2{{M}_{21}}\]
C) \[2{{M}_{12}}=2{{M}_{21}}\]
D) \[{{M}_{12}}=4{{M}_{21}}\]
Correct Answer: A
Solution :
From Faradays Law the induced emf in first solenoid \[{{\varepsilon }_{1}}=-\frac{d\phi }{dt}={{M}_{12}}=\frac{dI}{dt}\] ?. (i) (where J is the magnitude of current) And the induced emf in another solenoid \[{{\varepsilon }_{2}}=-\frac{d\phi }{dt}={{M}_{21}}=\frac{dI}{dt}\] ?. (ii) (Because length of both being equal carrying same magnitude of current) From Eqs. (i) and {ii) \[{{M}_{12}}={{M}_{21}}\]
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