Magnetic Effects of Current & Magnetism · JEE Main previous year questions

The magnetic moment of a bar magnet is $0.5{\text{ Am}}^2$. It is suspended in a uniform magnetic field of $8\times 10^{-2}\text{ T}$. The work done in rotating it from its most stable to most unstable position is:

1. A.$4\times 10^{-2}\text{ J}$
2. B.$16\times 10^{-2}\text{ J}$
3. C.$8\times 10^{-2}\text{ J}$
4. D.$\text{Zero}$

A regular polygon of 6 sides is formed by bending a wire of length $4\pi$ meter. If an electric current of $4\pi \sqrt{3}$ A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x\times 10^{-7}\mathrm{T}$. The value of $x$ is ____.

If frequency of electromagnetic wave is $60\text{ MHz}$ and it travels in air along $z$ direction then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other and the wavelength of the wave (in $\text{m}$ ) is :

1. A.2.5
2. B.5
3. C.10
4. D.2

A moving coil galvanometer has 100 turns and each turn has an area of $2.0{\text{ cm}}^2$. The magnetic field produced by the magnet is $0.01\text{ T}$ and the deflection in the coil is $0.05\text{ radian}$ when a current of $10\text{ mA}$ is passed through it. The torsional constant of the suspension wire is $x\times 10^{-5}\text{ N}-\text{m/rad}$. The value of $x$ is ________ .

A coil of 200 turns and area $0.20{\text{ m}}^2$ is rotated at half a revolution per second and is placed in uniform magnetic field of $0.01\text{ T}$ perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is $\frac{2\pi }{\beta }\text{ volt}$. The value of $\beta$ is ________ .

1. A.$iBR\hat{j}$
2. B.$-2iBR\hat{j}$
3. C.$2iBR\hat{j}$
4. D.$-iBR\hat{j}$

A coil is placed perpendicular to a magnetic field of $5000\mathrm{T}$. When the field is changed to $3000\mathrm{T}$ in $2\mathrm{s}$, an induced emf of $22\mathrm{V}$ is produced in the coil. If the diameter of the coil is $0.02\mathrm{m}$, then the number of turns in the coil is:

1. A.35
2. B.70
3. C.7
4. D.140

An electron moves through a uniform magnetic field $\vec{B}=B_0\hat{i}+2B_0\hat{j}T$. At a particular instant of time, the velocity of electron is $\vec{u}=3\hat{i}+5\hat{j}m/s$. If the magnetic force acting on electron is $\vec{F}=5e\hat{k}N$, where $e$ is the charge of electron, then the value of $B_0$ is ____ $T$.

Given below are two statements: Statement I: Electromagnetic waves carry energy as they travel through space and this energy is equally shared by the electric and magnetic fields. Statement II: When electromagnetic waves strike a surface, a pressure is exerted on the surface. In the light of the above statements, choose the most appropriate answer from the options given below:

1. A.Statement I is incorrect but Statement II is correct.
2. B.Both Statement I and Statement II are correct.
3. C.Statement I is correct but Statement II is incorrect.
4. D.Both Statement I and Statement II are incorrect.

Two circular coils $P$ and $Q$ of 100 turns each have same radius of $\pi \mathrm{cm}$. The currents in $P$ and $Q$ are $1A$ and $2A$ respectively. $P$ and $Q$ are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is $\sqrt{x}mT$, where $x=$ ____. [Use ${\mu }_0=4\pi \times 10^{-7}\mathrm{Tm}{\mathrm{A}}^{-1}$]

The horizontal component of earth's magnetic field at a place is $3.5\times 10^{-5}\text{ T}$. A very long straight conductor carrying current of $\sqrt{2}\text{ A}$ in the direction from South east to North West is placed. The force per unit length experienced by the conductor is _________ $\times 10^{-6}\text{ N/m}$.

A ceiling fan having 3 blades of length $80\text{ cm}$ each is rotating with an angular velocity of $1200\text{ rpm}$. The magnetic field of earth in that region is $0.5\text{G}$ and angle of dip is $30^{\circ }$. The emf induced across the blades is $\mathrm{N}\pi \times 10^{-5}\text{ V}$. The value of N is _________.

The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of $20\text{ cm}$ from its center is $1.5\times 10^{-5}\text{ T m}$. The magnetic moment of the dipole is _______ ${\text{A m}}^2$. (Given : $\frac{{\mu }_o}{4\pi }=10^{-7}{\text{TmA}}^{-1}$ )

A plane electromagnetic wave of frequency $35\text{ MHz}$ travels in free space along the $X$-direction. At a particular point (in space and time) $\vec{E}=9.6\hat{j}\text{ V/m}$. The value of magnetic field at this point is :

1. A.$9.6\hat{j}T$
2. B.$3.2\times 10^{-8}\hat{i}T$
3. C.$9.6\times 10^{-8}\hat{k}T$
4. D.$3.2\times 10^{-8}\hat{k}T$

Two particles $X$ and $Y$ having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describe circular paths of radii $R_1$ and $R_2$ respectively. The mass ratio of $X$ and $Y$ is :

1. A.$\left(\frac{R_1}{R_2}\right)$
2. B.$\left(\frac{R_2}{R_1}\right)$
3. C.${\left(\frac{R_2}{R_1}\right)}^2$
4. D.${\left(\frac{R_1}{R_2}\right)}^2$

A charge of $4.0\mu \mathrm{C}$ is moving with a velocity of $4.0\times 10^6{\text{ ms}}^{-1}$ along the positive $y$ axis under a magnetic field $\vec{B}$ of strength $(2\hat{k})\text{T}$. The force acting on the charge is $x\hat{i}N$. The value of $x$ is _________.

A horizontal straight wire $5\text{ m}$ long extending from east to west is falling freely at right angle to horizontal component of earths magnetic field $0.60\times 10^{-4}{\text{ Wbm}}^{-2}$. The instantaneous value of emf induced in the wire when its velocity is $10{\text{ ms}}^{-1}$ is _________ $\times 10^{-3}\text{ V}$.

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\vec{\text{E}}$ and $\vec{\text{B}}$ represent the electric and magnetic fields respectively, then the region of space may have : (A) $\text{E}=0$, $\text{B}=0$ (B) $\text{E}=0$, $\text{B}\ne 0$ (C) $\text{E}\ne 0$, $\text{B}=0$ (D) $\text{E}\ne 0$, $\text{B}\ne 0$ Choose the most appropriate answer from the options given below :

1. A.(A), (B) and (C) only
2. B.(A), (C) and (D) only
3. C.(A), (B) and (D) only
4. D.(B), (C) and (D) only

A rectangular loop of length $2.5\text{ m}$ and width $2\text{ m}$ is placed at $60^{\circ }$ to a magnetic field of $4\text{ T}$. The loop is removed from the field in $10\text{ sec}$. The average emf induced in the loop during this time is

1. A.$-2\text{ V}$
2. B.$+2\text{ V}$
3. C.$+1\text{ V}$
4. D.$-1\text{ V}$

An electron is moving along the positive $x$-axis. If the uniform magnetic field is applied parallel to the negative $z$-axis, then A. The electron will experience magnetic force along positive y-axis B. The electron will experience magnetic force along negative y-axis C. The electron will not experience any force in magnetic field D. The electron will continue to move along the positive x-axis E. The electron will move along circular path in magnetic field Choose the correct answer from the options given below:

1. A.A and E only
2. B.B and D only
3. C.B and E only
4. D.C and D only

A conducting circular loop is placed in a uniform magnetic field of $0.4\text{ T}$ with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of $1\text{ mm/s}$. The magnitude of induced emf in the loop at an instant when the radius of the loop is $2\text{ cm}$ will be _________ $\mu \mathrm{V}$.