Question

At time $t=0$ magnetic field of $1000 \mathrm{G}\mathrm{a}\mathrm{u}\mathrm{s}\mathrm{s}$ is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to $500 \mathrm{G}\mathrm{a}\mathrm{u}\mathrm{s}\mathrm{s},$ in the next $5\mathrm{s},$ then induced $\mathrm{E}\mathrm{M}\mathrm{F}$ in the loop is:

JEE Main 2020 (08 Jan Shift 1)

Options

• A: $56\mathrm{\mu }\mathrm{V}$
• B: $28\mathrm{\mu }\mathrm{V}$
• C: $48\mathrm{\mu }\mathrm{V}$
• D: $36\mathrm{\mu }\mathrm{V}$

Question

A loop $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}\mathrm{E}\mathrm{F}\mathrm{A}$ of straight edges has six corner points $A\left(0,0,0\right),B\left(5,0,0\right),C\left(5,5,0\right),D\left(0,5,0\right),E\left(0,5,5\right)$ and $F\left(0,0,5\right)$ . The magnetic field in this region is $\overrightarrow{B}=\left(3\widehat{i}+4\widehat{k}\right)T$ . The quantity of flux through the loop $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}\mathrm{E}\mathrm{F}\mathrm{A}$ (in $\mathrm{W}\mathrm{b}$ ) is _____________

JEE Main 2020 (07 Jan Shift 1)

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Question

Two concentric circular coils, $C_1$ and $C_2$, are placed in the $XY$ plane. $C_1$ has $500$turns, and a radius of $1 \mathrm{cm}$. $C_2$ has 200 turns and radius of $20 \mathrm{cm}\text{.} C_2$ carries a time dependent current $I\left(\mathit{t}\right)=\left(5t^2-2t+3\right)\mathrm{A}$ where $t$ is in s. The emf induced in $C_1\left(\mathrm{in} \mathrm{mV}\right)$ at the instant $t=1$s is $\frac{4}{x}.$ The value of $x$ is ..........

JEE Main 2020 (05 Sep Shift 1)

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Question

A planar loop of wire rotates in a uniform magnetic field. Initially, at $t=0$ , the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of $10\mathrm{}\mathrm{s}$ about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at:

JEE Main 2020 (07 Jan Shift 2)

Options

• A: $2.5 \mathrm{s}$ and $7.5 \mathrm{s}$
• B: $2.5 \mathrm{s}$ and $5.0 \mathrm{s}$
• C: $5.0 \mathrm{s}$ and $7.5 \mathrm{s}$
• D: $5.0 \mathrm{s}$ and $10.0 \mathrm{s}$

Question

For the given circuit the current $i$ through the battery when the key in closed and the steady state has been reached is

JEE Main 2021 (01 Sep Shift 2)

Options

• A: $10 \mathrm{A}$
• B: $6 \mathrm{A}$
• C: $25 \mathrm{A}$
• D: $0 \mathrm{A}$

Question

A square loop of side $20 \mathrm{cm}$ and resistance $1 \mathrm{\Omega }$ is moved towards right with a constant speed $v_0.$ The right arm of the loop is in a uniform magnetic field of $5 \mathrm{T}.$ The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value $4\mathrm{\Omega }.$ What should be the value of $v_0$ so that a steady current of $2 \mathrm{mA}$ flows in the loop ?

JEE Main 2021 (01 Sep Shift 2)

Options

• A: ${10}^{-2} \mathrm{cm} {\mathrm{s}}^{-1}$
• B: $1 \mathrm{m} {\mathrm{s}}^{-1}$
• C: $1 \mathrm{cm} {\mathrm{s}}^{-1}$
• D: ${10}^2 \mathrm{m} {\mathrm{s}}^{-1}$

Question

Consider an electrical circuit containing a two way switch $S.$ Initially $S$ is open and then $T_1$ is connected to $T_2.$ As the current in $R=6 \mathrm{\Omega }$ attains a maximum value of steady-state level, $T_1$ is disconnected from $T_2$ and immediately connected to $T_3.$ Potential drop across $r=3 \mathrm{\Omega }$ resistor immediately after $T_1$ is connected to $T_3$ is $\_\_\_\_\_\_\mathrm{V}.$ (Round off to the Nearest Integer)

JEE Main 2021 (27 Jul Shift 1)

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Question

A small square loop of wire of side $l$ is placed inside a large square loop of wire $L\left(L\gg l\right)$. 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 (25 Jul Shift 1)

Options

• A: $\frac{2\sqrt{2}{\mu }_0{L}^2}{\pi l}$
• B: $\frac{{\mu }_0{l}^2}{2\sqrt{2}\pi L}$
• C: $\frac{{\mu }_0{L}^2}{2\sqrt{2}\pi l}$
• D: $\frac{2\sqrt{2}{\mu }_0{l}^2}{\pi L}$

Question

In a series $LR$ circuit $X_L=R$ and power factor of the circuit is $P_1$. When capacitor with capacitance $C$ such that $X_L=X_C$ is put in series, the power factor becomes $P_2$. The ratio $\frac{P_1}{P_2}$ is

JEE Main 2022 (26 Jul Shift 1)

Options

• A: $\frac{1}{2}$
• B: $\frac{1}{\sqrt{2}}$
• C: $\frac{\sqrt{3}}{\sqrt{2}}$
• D: $2:1$

Question

Two coils of self inductance $L_1$ and $L_2$ 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 (26 Jun Shift 2)

Options

• A: $\frac{1}{L_1}+\frac{1}{L_2}+\frac{1}{M}$
• B: $L_1+L_2-2M$
• C: $L_1+L_2+M$
• D: $L_1+L_2+2M$

Question

A metallic conductor of length $1 \mathrm{m}$ rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity $5 \mathrm{rad} {\mathrm{s}}^{-1}$. If the horizontal component of earth's magnetic field is $0.2\times {10}^{-4} \mathrm{T}$, then emf induced between the two ends of the conductor is

JEE Main 2022 (26 Jun Shift 2)

Options

• A: $5\mu V$
• B: $50\mu \mathrm{V}$
• C: $5 \mathrm{m}V$
• D: $50 \mathrm{m}V$

Question

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius $R$ is placed inside a large square loop of wire of side $L(L\gg R)$. The loops are coplanar and their centres coincide :

JEE Main 2023 (29 Jan Shift 1)

Options

• A: $M=\frac{\sqrt{2}{\mu }_0{R}^2}{L}$
• B: $M=\frac{2\sqrt{2}{\mu }_{0}R}{L^2}$
• C: $M=\frac{2\sqrt{2}{\mu }_0{R}^2}{L}$
• D: $M=\frac{\sqrt{2}{\mu }_{0}R}{L^2}$

Question

The induced emf can be produced in a coil by

A. moving the coil with uniform speed inside uniform magnetic field

B. moving the coil with non uniform speed inside uniform magnetic field

C. rotating the coil inside the uniform magnetic field

D. changing the area of the coil inside the uniform magnetic field

Choose the correct answer from the options given below:

JEE Main 2023 (06 Apr Shift 1)

Options

• A: $B$ and $C$ only
• B: $A$ and $C$ only
• C: $C$ and $D$ only
• D: $B$ and $D$ only

Question

As per the given figure, if $\frac{\mathrm{d}I}{\mathrm{d}t}=-1 \mathrm{A} {\mathrm{s}}^{-1}$, then the value of $V_{\mathrm{AB}}$ at this instant will be ______ $\mathrm{V}$.

JEE Main 2023 (30 Jan Shift 1)

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Question

A $1 \mathrm{m}$ long metal rod $XY$ completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density $0.15 \mathrm{T}$. If the resistance of the circuit is $5 \Omega$, the force needed to move the rod in direction, as indicated, with a constant speed of $4 \mathrm{m} {\mathrm{s}}^{-1}$ will be _______${10}^{–3} \mathrm{N}$.

JEE Main 2023 (10 Apr Shift 1)

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Question

An insulated copper wire of $100$ turns is wrapped around a wooden cylindrical core of the cross-sectional area $24 {\mathrm{cm}}^2$. The two ends of the wire are connected to a resistor. The total resistance in the circuit is $12 \mathrm{\Omega }$. If an externally applied uniform magnetic field in the core along its axis changes from $1.5 \mathrm{T}$ in one direction to $1.5 \mathrm{T}$ in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be _____ $\mathrm{mC}$.

JEE Main 2023 (13 Apr Shift 2)

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Question

For the plane electromagnetic wave given by $E=E_0\sin (\omega t–kx)$ and $B=B_0\sin (\omega t-kx),$ the ratio of average electric energy density to average magnetic energy density is 

JEE Main 2023 (06 Apr Shift 1)

Options

• A: $\frac{1}{2}$
• B: $2$
• C: $4$
• D: $1$

Question

A rod of length $60 \mathrm{~cm}$ rotates with a uniform angular velocity $20 \mathrm{rad} \mathrm{s}^{-1}$ about its perpendicular bisector, in a uniform magnetic filed $0.5 T$. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is _____V.

JEE Main 2024 (04 Apr Shift 2)

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Question

A square loop PQRS having 10 turns, area $3.6 \times 10^{-3} \mathrm{~m}^2$ and resistance $100 \Omega$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $\mathrm{B}=0.5 \mathrm{~T}$ as shown. Work done in pulling the loop out of the field in $1.0 \mathrm{~s}$ is ______ $\times 10^{-6} \mathrm{~J}$.

JEE Main 2024 (08 Apr Shift 1)

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Question

When a coil is connected across a $20 \mathrm{~V}$ dc supply, it draws a current of $5 \mathrm{~A}$. When it is connected across $20 \mathrm{~V}, 50 \mathrm{~Hz}$ ac supply, it draws a current of $4 \mathrm{~A}$. The self inductance of the coil is ______ $\mathrm{mH}$. $($ Take $\pi=3$ )

JEE Main 2024 (09 Apr Shift 1)

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Question

Two coils have mutual inductance $0.002 \mathrm{H}$. The current changes in the first coil according to the relation $i=i_{0}sin\omega t$, where $i_0=5 \mathrm{A}$ and $\omega =50\pi$ $\mathrm{rad} {\mathrm{s}}^{-1}$. The maximum value of $\mathrm{emf}$ in the second coil is $\frac{\pi }{\alpha } \mathrm{V}$. The value of $\alpha$ is

JEE Main 2024 (27 Jan Shift 1)

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Question

A square loop of side $10 \mathrm{cm}$ and resistance $0.7 \mathrm{\Omega }$ is placed vertically in the east-west plane. A uniform magnetic field of $0.20 \mathrm{T}$ is set up across the plane in the north-east direction. The magnetic field is decreased to zero in $1 \mathrm{s}$ at a steady rate. Then, the magnitude of induced emf is $\sqrt{x}\times {10}^{-3} \mathrm{V}$. The value of $x$ is _______.

JEE Main 2024 (29 Jan Shift 1)

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Question

A rectangular loop of sides $12 \mathrm{cm}$ and $5 \mathrm{cm}$, with its sides parallel to the $x$-axis and $y$-axis respectively moves with a velocity of $5 \mathrm{cm} {\mathrm{s}}^{-1}$ in the positive $x$ axis direction, in a space containing a variable magnetic field in the positive $z$ direction. The field has a gradient of ${10}^{-3} \mathrm{T} {\mathrm{cm}}^{-1}$ along the negative $x$ direction and it is decreasing with time at the rate of ${10}^{-3} \mathrm{T} {\mathrm{s}}^{-1}.$ If the resistance of the loop is $6 \mathrm{m}\Omega$, the power dissipated by the loop as heat is ______ $\times {10}^{-9} \mathrm{W}.$

JEE Main 2024 (01 Feb Shift 1)

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Question

A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L$$\left(L=l^2\right)$. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $\sqrt{x}\times {10}^{-7} \mathrm{H}$, where $x=$______.

JEE Main 2024 (31 Jan Shift 1)

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