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
(1) \(\frac{μ_0}{4π}8 \sqrt 2 \frac{a^2}{b}\)
(2) \(\frac{μ_0}{4π}\frac{8 \sqrt 2}{a}\)
(3) \(\frac{μ_0}{4π}8 \sqrt 2 \frac{b^2}{a}\)
(4) \(\frac{μ_0}{4π}\frac{8 \sqrt 2}{b}\)
Correct answer: (1) \(\frac{μ_0}{4π}8 \sqrt 2 \frac{a^2}{b}\)
Explanation:
B = \(\Big[\frac{μ_0}{4π} \frac{I}{b/2} \times 2 sin 45 \Big] \times 4\)
φ = \(2 \sqrt 2 \frac{μ_0}{π} \frac{I}{b} \times a^2\)
∴ M = \(\frac{φ}{I}\) = \(\frac{2 \sqrt 2 μ_0 a^2}{πb}\) =
= \(\frac{μ_0}{4π}8 \sqrt 2 \frac{a^2}{b}\)