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

A monochromatic light is incident on a metallic plate having work function $\varphi$. An electron, emitted normally to the plate from a point A with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point $B$. The distance between $A$ and $B$ is : (Given : The magnitude of charge of an electron is e and mass is $\mathrm{m}$, $\mathrm{h}$ is Planck's constant and c is velocity of light. Take the magnetic field exists throughout the path of electron)

1. A.$\sqrt{2\mathrm{m}\left(\frac{\mathrm{h}c}{\lambda }-\varphi \right)}/eB$
2. B.$\sqrt{8\mathrm{m}\left(\frac{\mathrm{h}c}{\lambda }-\varphi \right)}/eB$
3. C.$\sqrt{\mathrm{m}(\mathrm{h}c/\lambda -\varphi )}/eB$
4. D.$2\sqrt{\mathrm{m}(\mathrm{h}c/\lambda -\varphi )}/eB$

Let $B_1$ be the magnitude of magnetic field at center of a circular coil of radius $R$ carrying current I. Let $B_2$ be the magnitude of magnetic field at an axial distance ' $x$ ' from the center. For $x:R=3:4$, $\frac{B_2}{B_1}$ is :

1. A.64 : 125
2. B.25 : 16
3. C.4 : 5
4. D.16 : 25

The relationship between the magnetic susceptibility ($\chi$) and the magnetic permeability ($\mu$) is given by : ( ${\mu }_0$ is the permeability of free space and ${\mu }_r$ is relative permeability)

1. A.$\chi =\frac{\mu }{{\mu }_0}-1$
2. B.$\chi =\frac{{\mu }_r}{{\mu }_0}+1$
3. C.$\chi ={\mu }_r+1$
4. D.$\chi =1-\frac{\mu }{{\mu }_0}$

A solenoid having area A and length ' $l$ ' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :

1. A.$\frac{{\mathrm{B}}^2\mathrm{Al}}{4{\mu }_0}$
2. B.$\frac{{\mathrm{B}}^2\mathrm{Al}}{2{\mu }_0}$
3. C.$\frac{{\mathrm{B}}^2\mathrm{Al}}{{\mu }_0}$
4. D.${\mathrm{B}}^2\mathrm{Al}$

An electron with mass ' $\mathrm{m}$ ' with an initial velocity $(t=0)\vec{\mathrm{v}}={\mathrm{v}}_0\hat{i}({\mathrm{v}}_0>0)$ enters a magnetic field $\vec{\mathrm{B}}={\mathrm{B}}_0\hat{j}$. If the initial de-Broglie wavelength at $t=0$ is ${\lambda }_0$ then its value after time ' t ' would be :

1. A.$\frac{{\lambda }_0}{\sqrt{1-\frac{e^2{\mathrm{B}}_0^2{t}^2}{{\mathrm{m}}^2}}}$
2. B.${\lambda }_0$
3. C.${\lambda }_0\sqrt{1+\frac{e^2{\mathrm{B}}_0^2{t}^2}{{\mathrm{m}}^2}}$
4. D.$\frac{{\lambda }_0}{\sqrt{1+\frac{e^2{\mathrm{B}}_0^2{t}^2}{{\mathrm{m}}^2}}}$

Match List - I with List - II. $$\begin{array}{ll}\text{List - I}& \text{List - II}\\ \text{(A) Magnetic induction}& {\text{(I) Ampere meter}}^2\\ \text{(B) Magnetic intensity}& \text{(II) Weber}\\ \text{(C) Magnetic flux}& \text{(III) Gauss}\\ \text{(D) Magnetic moment}& {\text{(IV) Ampere meter}}^{-1}\end{array}$$ Choose the correct answer from the options given below:

1. A.(A)-(III), (B)-(IV), (C)-(II), (D)-(I)
2. B.(A)-(III), (B)-(II), (C)-(I), (D)-(IV)
3. C.(A)-(III), (B)-(IV), (C)-(I), (D)-(II)
4. D.(A)-(I), (B)-(II), (C)-(III), (D)-(IV)

The magnetic field inside a 200 turns solenoid of radius $10\mathrm{cm}$ is $2.9\times 10^{-4}\mathrm{Tesla}$. If the solenoid carries a current of $0.29\mathrm{A}$ , then the length of the solenoid is ____ $\pi \mathrm{cm}$.

A current of $5\mathrm{A}$ exists in a square loop of side $\frac{1}{\sqrt{2}}\mathrm{m}$. Then the magnitude of the magnetic field $B$ at the centre of the square loop will be $p\times 10^{-6}\mathrm{T}$. where, value of p is ____ [ Take ${\mu }_0=4\pi \times 10^{-7}\mathrm{T}\mathrm{m}{\mathrm{A}}^{-1}$ ].

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : An electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path. Reason (R) : The magnetic field in that region is along the direction of velocity of the electron. In the light of the above statements, choose the correct answer from the options given below :

1. A.(A) is true but (R) is false
2. B.Both (A) and (R) are true and (R) is the correct explanation of (A)
3. C.Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
4. D.(A) is false but (R) is true

1. A.
2. B.
3. C.
4. D.

A tightly wound long solenoid carries a current of 1.5 A . An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns . The number of turns per metre in the solenoid is ________. [Take mass of electron ${\mathrm{m}}_e=9\times 10^{-31}\text{ kg}$, charge of electron $|{\mathrm{q}}_e|=1.6\times 10^{-19}\text{C}$, ${\mu }_0=4\pi \times 10^{-7}\frac{\mathrm{N}}{{\mathrm{A}}^2}$, $1\text{ ns}=10^{-9}\text{ s}$]

Match List - I with List - II | | List - I | | List - II | |---|---|---|---| | (A) | Permeability of free space | (I) | $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$ | | (B) | Magnetic field | (II) | $\left[{\mathrm{MT}}^{-2}{\mathrm{A}}^{-1}\right]$ | | (C) | Magnetic moment | (III) | $\left[{\mathrm{MLT}}^{-2}{\mathrm{A}}^{-2}\right]$ | | (D) | Torsional constant | (IV) | $\left[{\mathrm{L}}^2\mathrm{A}\right]$ | Choose the correct answer from the options given below :

1. A.(A)-(III), (B)-(II), (C)-(IV), (D)-(I)
2. B.(A) – (I), (B) – (IV), (C) – (II), (D) – (III)
3. C.(A) – (II), (B) – (I), (C) – (III), (D) – (IV)
4. D.(A)-(IV), (B)-(III), (C)-(I), (D)-(II)

Given below are two statements : Statement (I) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account Statement (II) : Ampere's circuital law does not depend on Biot-Savart's law. In the light of the above statements, choose the correct answer from the options given below :

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

A square loop of edge length $2\text{ m}$ carrying current of $2\text{ A}$ is placed with its edges parallel to the $x$-$y$ axis. A magnetic field is passing through the $x$-$y$ plane and expressed as $\vec{B}=B_0(1+4x)\hat{k}$, where $B_0=5\text{ T}$. The net magnetic force experienced by the loop is ______ $\text{N}$.

A proton and a deuteron ($q=+\mathrm{e},m=2.0\mathrm{u}$) having same kinetic energies enter a region of uniform magnetic field $\vec{B}$, moving perpendicular to $\vec{B}$. The ratio of the radius $r_d$ of deuteron path to the radius $r_p$ of the proton path is:

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

1. A.zero
2. B.$4.5\mathrm{mV}$
3. C.$0.3\mathrm{mV}$
4. D.$3\mathrm{mV}$

A straight magnetic strip has a magnetic moment of $44{\mathrm{Am}}^2$. If the strip is bent in a semicircular shape, its magnetic moment will be ____ ${\mathrm{Am}}^2$. (given $\pi =\frac{22}{7}$)

Paramagnetic substances: A. align themselves along the directions of external magnetic field. B. attract strongly towards external magnetic field. C. has susceptibility little more than zero. D. move from a region of strong magnetic field to weak magnetic field. Choose the most appropriate answer from the options given below:

1. A.A, B, C Only
2. B.A, C Only
3. C.A, B, C, D
4. D.B, D Only

A long straight wire of radius $a$ carries a steady current $\mathrm{I}$. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\frac{a}{2}$ and $2a$ from axis of the wire is :

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

The coercivity of a magnet is $5\times 10^{3}A/m$. The amount of current required to be passed in a solenoid of length $30\mathrm{cm}$ and the number of turns $150$, so that the magnet gets demagnetised when inside the solenoid is ____ $\mathrm{A}$.

1. A.(A)-(III), (B)-(IV), (C)- (I), (D)-(II)
2. B.(A)-(III), (B)-(I), (C)-(IV), (D)-(II)
3. C.(A)-(IV), (B)-(I), (C)-(III), (D)-(II)
4. D.(A)-(I), (B)-(III), (C)-(II), (D)-(IV)

A coil having 100 turns, area of $5\times 10^{-3}{\text{ m}}^2$, carrying current of $1\text{ mA}$ is placed in uniform magnetic field of $0.20\text{ T}$ such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through $90^{\circ }$ is ________ $\mu \text{J}$.

A solenoid of length $0.5\mathrm{m}$ has a radius of $1\mathrm{cm}$ and is made up of '$\mathrm{m}$' number of turns. It carries a current of $5\mathrm{A}$. If the magnitude of the magnetic field inside the solenoid is $6.28\times 10^{-3}\mathrm{T}$ then the value of $\mathrm{m}$ is ____.

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :

1. A.the electron will experience a force at $45^{\circ }$ to the axis and execute a helical path.
2. B.the electron will be accelerated along the axis.
3. C.the electron path will be circular about the axis.
4. D.the electron will continue to move with uniform velocity along the axis of the solenoid.