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STD 12 -6. Electromagnetic induction — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 -6. Electromagnetic induction4 Marks
MCQ
What is the mutual inductance of a two-loop system as shown with centre separation l
  • A
    $\frac{{{\mu _0}\pi {a^4}}}{{8{l^3}}}$
  • B
    $\frac{{{\mu _0}\pi {a^4}}}{{4{l^3}}}$
  • C
    $\frac{{{\mu _0}\pi {a^4}}}{{6{l^3}}}$
  • ✓
    $\frac{{{\mu _0}\pi {a^4}}}{{2{l^3}}}$
✓

Answer

Correct option: D.
$\frac{{{\mu _0}\pi {a^4}}}{{2{l^3}}}$
d
(d)Magnetic field at the location of coil $(2)$ produced due to coil $(1)$

${B_1} = \frac{{{\mu _o}}}{{4\pi }}.\frac{{2M}}{{{l^3}}}$
Flux linked with coil $(2)$
${\phi _2} = {B_1}{A_2} = \frac{{{\mu _o}}}{{4\pi }}\frac{{2i\;(\pi {a^2})}}{{{l^3}}} \times (\pi {a^2})$
Also ${\phi _2} = Mi$ $ \Rightarrow M = \frac{{{\mu _o}\pi {a^4}}}{{2{l^3}}}$

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