JEE MAIN - Physics (2008 - No. 7)
Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $$A=$$ $$10\,\,c{m^2}$$ and length $$=20$$ $$cm$$ . If one of the solenoid has $$300$$ turns and the other $$400$$ turns, their mutual inductance is
$$\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,Tm\,{A^{ - 1}}} \right)$$
$$\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,Tm\,{A^{ - 1}}} \right)$$
$$2.4\pi \times {10^{ - 5}}H$$
$$4.8\pi \times {10^{ - 4}}H$$
$$4.8\pi \times {10^{ - 5}}H$$
$$2.4\pi \times {10^{ - 4}}H$$
Explanation
$$M = {{{\mu _0}{N_1}{N_2}A} \over \ell }$$
$$ = {{4\pi \times {{10}^{ - 7}} \times 300 \times 400 \times 100 \times {{10}^{ - 4}}} \over {0.2}}$$
$$ = 2.4\pi \times {10^{ - 4}}H$$
$$ = {{4\pi \times {{10}^{ - 7}} \times 300 \times 400 \times 100 \times {{10}^{ - 4}}} \over {0.2}}$$
$$ = 2.4\pi \times {10^{ - 4}}H$$
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