A small square loop of side a and one turn is placed inside a...

A small square loop of side

a

and one turn is placed inside a larger square loop of side

b

and one turn

( b ≫ a ) .

The two loops are coplanar with their centres coinciding. If a current

I

is passed in the square loop of side

b,

then the coefficient of mutual inductance between the two loops is : A small square loop of side a and one turn is placed inside a larger square loop of side b and one turn ( b ≫ a ) . The

A small square loop of side a and one turn is placed inside a larger square loop of side b and one turn ( b ≫ a ) . The

Options

A $\dfrac{{\mu}_{0}}{4\pi}8\sqrt{2}\dfrac{{a}^{2}}{b}$
B $\dfrac{{\mu}_{0}}{4\pi}8\sqrt{2}\dfrac{{b}^{2}}{a}$
C $\dfrac{{\mu}_{0}}{4\pi}\dfrac{8\sqrt{2}}{b}$
D $\dfrac{{\mu}_{0}}{4\pi}\dfrac{8\sqrt{2}}{a}$

Correct answer

A. $\dfrac{{\mu}_{0}}{4\pi}8\sqrt{2}\dfrac{{a}^{2}}{b}$

Step-by-step solution

B = 4 \times \dfrac{{\mu}_{0}i}{4\pi\left(\dfrac{b}{2}\right)}

\sqrt{2} ⇒ B = \dfrac{2\sqrt{2}{\mu}_{0}i}{\pib}

<br />

⇒ ϕ = MI ⇒ BA = MI

<br />

⇒ \dfrac{2\sqrt{2}{\mu}_{0}i}{\pib} \cdot {a}^{2} = Mi ⇒ M = \dfrac{2\sqrt{2}{\mu}_{0}{a}^{2}}{\pib} = \dfrac{{\mu}_{0}}{4\pi}\dfrac{8\sqrt{2}{a}^{2}}{b}

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