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

1. A.A-Flux, B-Power dissipated, C-EMF
2. B.A-Flux, B-EMF, C-Power dissipated
3. C.A-Power dissipated, B-Flux, C-EMF
4. D.A-EMF, B-Power dissipated, C-Flux

The radiation corresponding to $3\to 2$ transition of a hydrogen atom falls on a gold surface to generate photoelectrons. The electrons are passed through a magnetic field of $5\times 10^{-4}\text{ T}$. Assume that the radius of the largest circular path followed by these electrons is $7\text{ mm}$, the work function of the metal is : (Mass of electron $=9.1\times 10^{-31}\text{ kg}$)

1. A.$1.36\text{ eV}$
2. B.$1.88\text{ eV}$
3. C.$0.82\text{ eV}$
4. D.$0.16\text{ eV}$

1. A.12T
2. B.6T
3. C.9T
4. D.1T

A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.

1. A.Loop assumes circular shape with its plane normal to the field.
2. B.Loop assumes circular shape with its plane parallel to the field.
3. C.Wire gets stretched to become straight.
4. D.Shape of the loop remains unchanged.

A proton and an $\alpha$-particle, having kinetic energies $K_p$ and $K_{\alpha }$ respectively, enter into a magnetic field at right angles. The ratio of the radii of trajectory of proton to that of $\alpha$-particle is $2:1$. The ratio of $K_p:K_{\alpha }$ is :

1. A.$8:1$
2. B.$4:1$
3. C.$1:8$
4. D.$1:4$

Which of the following statements are correct? (A) Electric monopoles do not exist whereas magnetic monopoles exist. (B) Magnetic field lines due to a solenoid at its ends and outside cannot be completely straight and confined. (C) Magnetic field lines are completely confined within a toroid. (D) Magnetic field lines inside a bar magnet are not parallel. (E) $\chi =-1$ is the condition for a perfect diamagnetic material, where $\chi$ is its magnetic susceptibility. Choose the correct answer from the options given below :

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

1. A.Both $I_1$ and $I_2$ are in clockwise direction
2. B.$I_1$ is in clockwise direction and $I_2$ is in anticlockwise direction
3. C.$I_1$ is in anticlockwise direction and $I_2$ is in clockwise direction
4. D.Both $I_1$ and $I_2$ are in anticlockwise direction

A bar magnet of length 14 cm is placed in the magnetic meridian with its north pole pointing towards the geographic north pole. A neutral point is obtained at a distance of 18 cm from the center of the magnet. If ${\mathrm{B}}_{\mathrm{H}}=0.4\mathrm{G}$, the magnetic moment of the magnet is : $(1\mathrm{G}=10^{-4}\mathrm{T})$

1. A.$2.880\times 10^2\mathrm{J}{\mathrm{T}}^{-1}$
2. B.$2.880\mathrm{J}{\mathrm{T}}^{-1}$
3. C.$2.880\times 10^3\mathrm{J}{\mathrm{T}}^{-1}$
4. D.$28.80\mathrm{J}{\mathrm{T}}^{-1}$

In a ferromagnetic material, below the curie temperature, a domain is defined as :

1. A.a macroscopic region with zero magnetization.
2. B.a macroscopic region with saturation magnetization.
3. C.a macroscopic region with randomly oriented magnetic dipoles.
4. D.a macroscopic region with consecutive magnetic dipoles oriented in opposite direction.

A particle of charge q and mass m is moving with a velocity $-v\hat{i}$ ($v\ne 0$) towards a large screen placed in the Y - Z plane at a distance d. If there is a magnetic field $\vec{B}=B_0\hat{k}$, the maximum value of v for which the particle will not hit the screen is :

1. A.$\frac{2qd{B}_0}{m}$
2. B.$\frac{qd{B}_0}{3m}$
3. C.$\frac{qd{B}_0}{2m}$
4. D.$\frac{qd{B}_0}{m}$

A charged particle going around in a circle can be considered to be a current loop. A particle of mass m carrying charge q is moving in a plane with speed v under the influence of magnetic field $\vec{B}$. The magnetic moment of this moving particle:

1. A.$\frac{m{v}^2\vec{B}}{2B^2}$
2. B.$-\frac{m{v}^2\vec{B}}{2B^2}$
3. C.$-\frac{m{v}^2\vec{B}}{B^2}$
4. D.$-\frac{m{v}^2\vec{B}}{2\pi B^2}$

A charged particle carrying charge $1\mu \mathrm{C}$ is moving with velocity $(2\hat{i}+3\hat{j}+4\hat{k})\mathrm{m}{\mathrm{s}}^{-1}$. If an external magnetic field of $(5\hat{i}+3\hat{j}-6\hat{k})\times 10^{-3}\mathrm{T}$ exists in the region where the particle is moving then the force on the particle is $\vec{F}\times 10^{-9}\mathrm{N}$. The vector $\vec{F}$ is :

1. A.$-0.30\hat{i}+0.32\hat{j}-0.09\hat{k}$
2. B.$-300\hat{i}+320\hat{j}-90\hat{k}$
3. C.$-30\hat{i}+32\hat{j}-9\hat{k}$
4. D.$-3.0\hat{i}+3.2\hat{j}-0.9\hat{k}$

Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of $\frac{{\mu }_{0}I}{\pi }$ is :

1. A.$250\sqrt{3}$
2. B.$5\sqrt{3}$
3. C.$500\sqrt{3}$
4. D.$50\sqrt{3}$

1. A.$\vec{B}$
2. B.zero
3. C.much large than $|\vec{B}|$ and parallel to $\vec{B}$
4. D.much large than $|\vec{B}|$ but opposite to $\vec{B}$

A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate $\frac{dB}{dt}=0.032\mathrm{T}{\mathrm{s}}^{-1}$. The induced current in the loop is close to (Resistivity of the metal wire is $1.23\times 10^{-8}\Omega \mathrm{m}$)

1. A.0.53 A
2. B.0.43 A
3. C.0.34 A
4. D.0.61 A

A plane electromagnetic wave, has frequency of $2.0\times 10^{10}\text{ Hz}$ and its energy density is $1.02\times 10^{-8}{\text{ J/m}}^3$ in vacuum. The amplitude of the magnetic field of the wave is close to ($\frac{1}{4\pi {\epsilon }_0}=9\times 10^9\frac{\mathrm{N}{\mathrm{m}}^2}{{\mathrm{C}}^2}$ and speed of light $=3\times 10^8{\text{ ms}}^{-1}$)

1. A.190 nT
2. B.150 nT
3. C.160 nT
4. D.180 nT

A beam of protons with speed $4\times 10^5{\text{ ms}}^{-1}$ enters a uniform magnetic field of 0.3 T at an angle of $60^{\circ }$ to the magnetic field. The pitch of the resulting helical path of protons is close to : (Mass of the proton $=1.67\times 10^{-27}\text{ kg}$, charge of the proton $=1.69\times 10^{-19}\text{ C}$)

1. A.2 cm
2. B.12 cm
3. C.5 cm
4. D.4 cm

A circular coil of radius $10\mathrm{cm}$ is placed in a uniform magnetic field of $3.0\times 10^{-5}\mathrm{T}$ with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in $0.2\mathrm{s}$. The maximum value of EMF induced (in $\mu \mathrm{V}$) in the coil will be close to the integer ____.

1. A.0.22 m
2. B.0.11 m
3. C.0.88 m
4. D.0.44 m

1. A.$\sqrt{2}\mathrm{abI}$, along $\left(\frac{\hat{j}}{\sqrt{5}}+\frac{2\hat{k}}{\sqrt{5}}\right)$
2. B.$\mathrm{abI}$, along $\left(\frac{\hat{j}}{\sqrt{5}}+\frac{2\hat{k}}{\sqrt{5}}\right)$
3. C.$\sqrt{2}\mathrm{abI}$, along $\left(\frac{\hat{j}}{\sqrt{2}}+\frac{\hat{k}}{\sqrt{2}}\right)$
4. D.$\mathrm{abI}$, along $\left(\frac{\hat{j}}{\sqrt{2}}+\frac{\hat{k}}{\sqrt{2}}\right)$

A long, straight wire of radius a carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance $\frac{a}{3}$ and $2a$, respectively from the axis of the wire is :

1. A.2
2. B.$\frac{1}{2}$
3. C.$\frac{3}{2}$
4. D.$\frac{2}{3}$

Radiation, with wavelength $6561\text{ A˚}$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3\times 10^{-4}\text{ T}$. If the radius of the largest circular path followed by the electrons is $10\text{ mm}$, the work function of the metal is close to :

1. A.1.8eV
2. B.0.8eV
3. C.1.1eV
4. D.1.6eV

1. A.$\frac{e{\mu }_{0}nIR}{4m}$
2. B.$\frac{e{\mu }_{0}nIR}{m}$
3. C.$\frac{e{\mu }_{0}nIR}{2m}$
4. D.$\frac{2e{\mu }_{0}nIR}{m}$

A plane electromagnetic wave is propagating along the direction $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$, with its polarization along the direction $\hat{k}$. The correct form of the magnetic field of the wave would be (here ${\mathrm{B}}_0$ is an appropriate constant) :

1. A.$B_0\frac{\hat{i}-\hat{j}}{\sqrt{2}}\cos \left(\omega t-k\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)$
2. B.$B_0\frac{\hat{i}+\hat{j}}{\sqrt{2}}\cos \left(\omega t-k\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)$
3. C.$B_0\frac{\hat{j}-\hat{i}}{\sqrt{2}}\cos \left(\omega t+k\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)$
4. D.$B_0\hat{k}\cos \left(\omega t-k\frac{\hat{i}+\hat{j}}{\sqrt{2}}\right)$

Proton with kinetic energy of 1MeV moves from south to north. It gets an acceleration of $10^{12}{\text{ m/s}}^2$ by an applied magnetic field (west to east). The value of magnetic field : (Rest mass of proton is $1.6\times 10^{-27}\text{ kg}$) :

1. A.0.71mT
2. B.7.1mT
3. C.0.071mT
4. D.71mT