JEE Main Electromagnetic Induction PYQ

6. (JEE Main 2022 (Online) 25th July Morning Shift)

A small square loop of wire of side $l$ is placed inside a large square loop of wire $L (L >> l)$ . Both loops are coplanar and their centres coincide at point $O$ as shown in figure. The mutual inductance of the system is :

JEE Main 2022 (Online) 25th July Morning Shift Physics - Electromagnetic Induction Question 47 English

A. $\frac{2 \sqrt{2} μ_{0} L^{2}}{π l}$

B. $\frac{μ_{0} l^{2}}{2 \sqrt{2} π L}$

C. $\frac{2 \sqrt{2} μ_{0} l^{2}}{π L}$

D. $\frac{μ_{0} L^{2}}{2 \sqrt{2} π l}$

Correct Option is (A)

We know $ϕ = M i$

Let i current be flowing in the larger loop

$\Rightarrow ϕ ≃ [4 \times \frac{μ_{0} i}{4 π (L / 2)} [\sin 45^{\circ} + \sin 45^{\circ}]] \times$ Area

$= \frac{2 \sqrt{2} μ_{0} i}{π L} \times I^{2}$

$\Rightarrow M = \frac{ϕ}{i} = \frac{2 \sqrt{2} μ_{0} I^{2}}{π L}$

7. (JEE Main 2022 (Online) 26th June Evening Shift)

Two coils of self inductance L₁ and L₂ are connected in series combination having mutual inductance of the coils as M. The equivalent self inductance of the combination will be :

JEE Main 2022 (Online) 26th June Evening Shift Physics - Electromagnetic Induction Question 53 English

A. $\frac{1}{L_{1}} + \frac{1}{L_{2}} + \frac{1}{M}$

B. $L_{1} + L_{2} + M$

C. $L_{1} + L_{2} + 2 M$

D. $L_{1} + L_{2} - 2 M$

Correct Option is (D)

Self inductances are in series but their mutual inductances are linked oppositely so equivalent self inductance

L = L₁ + L₂ $-$ M $-$ M = L₁ + L₂ $-$ 2M

8. (JEE Main 2021 (Online) 31st August Morning Shift)

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. $\frac{μ_{0}}{4 π} 8 \sqrt{2} \frac{a^{2}}{b}$

B. $\frac{μ_{0}}{4 π} \frac{8 \sqrt{2}}{a}$

C. $\frac{μ_{0}}{4 π} 8 \sqrt{2} \frac{b^{2}}{a}$

D. $\frac{μ_{0}}{4 π} \frac{8 \sqrt{2}}{b}$

Correct Option is (A)

JEE Main 2021 (Online) 31st August Morning Shift Physics - Electromagnetic Induction Question 58 English Explanation
$B = [\frac{μ_{0}}{4 π} \frac{I}{b / 2} \times 2 \sin 45] \times 4$

$ϕ = 2 \sqrt{2} \frac{μ_{0}}{π} \frac{I}{b} \times a^{2}$

$∴$ $M = \frac{ϕ}{I} = \frac{2 \sqrt{2} μ_{0} a^{2}}{π b} = \frac{μ_{0}}{4 π} 8 \sqrt{2} \frac{a^{2}}{b}$

Option (a)

9. (JEE Main 2019 (Online) 9th April Evening Slot)

Two coils 'P' and 'Q' are separated by some distance. When a current of 3 A flows through coil 'P', a magnetic flux of 10–3 Wb passes through 'Q'. No current is passed through 'Q'. When no current passes through 'P' and a current of 2 A passes through 'Q', the flux through 'P' is :-

A.3.67 × 10^–4 Wb

B.3.67 × 10^–3 Wb

C.6.67 × 10^–4 Wb

D.6.67 × 10^–3 Wb

Correct option is (C)

Mutual induction

$ϕ_{q} = M I_{p}$

10^–3 = M(3)

$\Rightarrow M = \frac{1}{3} \times 10^{- 3}$

$ϕ_{p} = M I_{q}$

$\Rightarrow ϕ_{p} = 6.67 \times 10^{- 4} W b$

10. (JEE Main 2019 (Online) 11th January Morning Slot)

There are two long co-axial solenoids of same length $l$ . The inner and outer coils have radii r₁ and r₂ and number of turns per unit length n₁ and n₂, respectively. The ratio of mutual inductance to the self - inductance of the inner-coil is :

A.There are two long co-axial solenoids of same length $l$ . The inner and outer coils have radii r₁ and r₂ and number of turns per unit length n₁ and n₂, respectively. The ratio of mutual inductance to the self - inductance of the inner-coil is :

B. $\frac{n_{2}}{n_{1}}$

C. $\frac{n_{1}}{n_{2}}$

D. $\frac{n_{2}}{n_{1}} . \frac{r_{1}}{r_{2}}$

Correct option is (B)

$M = μ_{0} n_{1} n_{2} π r_{1}^{2}$

$L = μ_{0} n_{1}^{2} π r_{1}^{2}$

$\Rightarrow \frac{M}{L} = \frac{n_{2}}{n_{1}}$