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

1. A.$F=0$
2. B.$F\propto \left(\frac{a}{d}\right)$
3. C.$F\propto \left(\frac{a^2}{d^3}\right)$
4. D.$F\propto {\left(\frac{a}{d}\right)}^2$

A plane electromagnetic wave of frequency $50\text{ MHz}$ travels in free space along the positive x-direction. At a particular point in space and time, $\vec{E}=6.3\hat{j}\text{ V/m}$. The corresponding magnetic field $\vec{B}$, at that point will be :

1. A.$18.9\times 10^{-8}\hat{k}\text{ T}$
2. B.$2.1\times 10^{-8}\hat{k}\text{ T}$
3. C.$6.3\times 10^{-8}\hat{k}\text{ T}$
4. D.$18.9\times 10^8\hat{k}\text{ T}$

A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 m, 100 turns, and carrying a current of 5.2 A. The coercivity of the bar magnet is :

1. A.285 A/m
2. B.2600 A/m
3. C.520 A/m
4. D.1200 A/m

A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B. When it is rotated with an angular velocity $\omega$, the maxium e.m.f. induced in the coil will be:

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

A plane electromagnetic wave of wavelength $\lambda$ has an intensity I. It is propagatting along the positive Y-direction. The allowed expressions for the electric and magnetic fields are givn by :

1. A.$\vec{E}=\sqrt{\frac{2I}{{ϵ}_{0}C}}\cos \left[\frac{2\pi }{\lambda }(y-ct)\right]\hat{k};\vec{B}=+\frac{1}{c}E\hat{i}$
2. B.$\vec{E}=\sqrt{\frac{2I}{{ϵ}_{0}c}}\cos \left[\frac{2\pi }{\lambda }(y+ct)\right]\hat{k};\vec{B}=-\frac{1}{c}E\hat{i}$
3. C.$\vec{E}=\sqrt{\frac{I}{{ϵ}_{0}c}}\cos \left[\frac{2\pi }{\lambda }(y-ct)\right]\hat{k};\vec{B}=-\frac{1}{c}E\hat{i}$
4. D.$\vec{E}=\sqrt{\frac{I}{{ϵ}_{0}c}}\cos \left[\frac{2\pi }{\lambda }(y-ct)\right]\hat{i};\vec{B}=\frac{1}{c}E\hat{k}$

A monochromatic beam of light has a frequency $\nu =\frac{3}{2\pi }\times 10^{12}Hz$ and is propagating along the direction $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$. It is polarized along the $\hat{k}$ direction. The acceptable form for the magnetic field is :

1. A.$\frac{E_o}{C}\frac{(\hat{i}-\hat{j})}{\sqrt{2}}\cos \left[10^4\frac{(\hat{i}+\hat{j})}{\sqrt{2}}\cdot \vec{r}-(3\times 10^{12})t\right]$
2. B.$\frac{E_o}{C}\frac{(\hat{i}-\hat{j})}{\sqrt{2}}\cos \left[10^4\frac{(\hat{i}-\hat{j})}{\sqrt{2}}\cdot \vec{r}-(3\times 10^{12})t\right]$
3. C.$\frac{E_o}{C}\hat{k}\cos \left[10^4\frac{(\hat{i}+\hat{j})}{\sqrt{2}}\cdot \vec{r}+(3\times 10^{12})t\right]$
4. D.$\frac{E_o}{C}\frac{(\hat{i}+\hat{j}+\hat{k})}{\sqrt{3}}\cos \left[10^4\frac{(\hat{i}+\hat{j})}{\sqrt{2}}\cdot \vec{r}+(3\times 10^{12})t\right]$

1. A.$\frac{8N{\mu }_{0}I}{5^{1/2}R}$
2. B.$\frac{8N{\mu }_{0}I}{5^{3/2}R}$
3. C.$\frac{4N{\mu }_{0}I}{5^{1/2}R}$
4. D.$\frac{4N{\mu }_{0}I}{5^{3/2}R}$

1. A.$1mA$
2. B.$2mA$
3. C.$20\mu A$
4. D.$40\mu A$

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii $r_e,r_p,r_{\alpha }$ respectively in a uniform magnetic field B. The relation between $r_e,r_p,r_{\alpha }$ is:

1. A.$r_e<r_{\alpha }<r_p$
2. B.$r_e>r_p=r_{\alpha }$
3. C.$r_e<r_p=r_{\alpha }$
4. D.$r_e<r_p<r_{\alpha }$

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

A magnetic dipole in a constant magnetic field has :

1. A.maximum potential energy when the torque is maximum.
2. B.zero potential energy when the torque is minimum.
3. C.zero potential energy when the torque is maximum.
4. D.minimum potential energy when the torque is maximum.

Two identical wires $A$ and $B$, each of length '$l$', carry the same current $I$. Wire $A$ is bent into a circle of radius $R$ and wire $B$ is bent to form a square of side '$a$'. If $B_A$ and $B_B$ are the values of magnetic fields at the centres of the circle and square respectively, then the ratio $\frac{B_A}{B_B}$ is:

1. A.$\frac{{\pi }^2}{16}$
2. B.$\frac{{\pi }^2}{8\sqrt{2}}$
3. C.$\frac{{\pi }^2}{8}$
4. D.$\frac{{\pi }^2}{16\sqrt{2}}$

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

Two coaxial solenoids of different radius carry current $I$ in the same direction. ${\vec{F}}_1$ be the magnetic force on the inner solenoid due to the outer one and ${\vec{F}}_2$ be the magnetic force on the outer solenoid due to the inner one. Then :

1. A.${\vec{F}}_1\text{ is radially in wards and }{\vec{F}}_2=0$
2. B.${\vec{F}}_1\text{ is radially outwards and }{\vec{F}}_2=0$
3. C.${\vec{F}}_1={\vec{F}}_2=0$
4. D.${\vec{F}}_1\text{ is radially inwards and }{\vec{F}}_2\text{ is radially outards}$

The coercivity of a small magnet where the ferromagnet gets demagnetized is $3\times 10^3\mathrm{A}{\mathrm{m}}^{-1}$. The current required to be passed in a solenoid of length $10\mathrm{cm}$ and number of turns $100$, so that the magnet gets demagnetized when inside the solenoid, is :

1. A.$30\mathrm{mA}$
2. B.$60\mathrm{mA}$
3. C.$3\mathrm{A}$
4. D.$6\mathrm{A}$

The radiation corresponding to $3\to 2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field $3\times 10^{-4}\mathrm{T}$. If the radius of the larger circular path followed by these electrons is $10.0\mathrm{mm}$, the work function of the metal is close to:

1. A.$1.8\mathrm{eV}$
2. B.$1.1\mathrm{eV}$
3. C.$0.8\mathrm{eV}$
4. D.$1.6\mathrm{eV}$

This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: A charged particle is moving at right angle to a static magnetic field. During the motion the kinetic energy of the charge remains unchanged. Statement 2: Static magnetic field exert force on a moving charge in the direction perpendicular to the magnetic field.

1. A.Statement 1 is false, Statement 2 is true.
2. B.Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.
3. C.Statement 1 is true, Statement 2 is false.
4. D.Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

The magnetic force acting on charged particle of charge $2\mu \mathrm{C}$ in magnetic field of $2\mathrm{T}$ acting in $y$-direction, when the particle velocity is $(2\hat{i}+3\hat{j})\times 10^6\mathrm{m}{\mathrm{s}}^{-1}$ is

1. A.$8\mathrm{N}$ in $z$-direction
2. B.$8\mathrm{N}$ in $y$-direction
3. C.$4\mathrm{N}$ in $y$-direction
4. D.$4\mathrm{N}$ in $z$-direction

A bar magnet of length $6\mathrm{cm}$ has a magnetic moment of $4\mathrm{J}{\mathrm{T}}^{-1}$. Find the strength of magnetic field at a distance of $200\mathrm{cm}$ from the centre of the magnet along its equatorial line.

1. A.$4\times 10^{-8}\mathrm{tesla}$
2. B.$3.5\times 10^{-8}\mathrm{tesla}$
3. C.$5\times 10^{-8}\mathrm{tesla}$
4. D.$3\times 10^{-8}\mathrm{tesla}$

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

1. A.$\frac{{\mu }_{0}I(b-a)}{24ab}$
2. B.$\frac{{\mu }_{0}I}{4\pi }\left[\frac{b-a}{ab}\right]$
3. C.$\frac{{\mu }_{0}I}{4\pi }[2(b-a)+\pi /3(a+b)]$
4. D.zero

Needles $N_1,N_2$ and $N_3$ are made of a ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A magnet when brought close to them will

1. A.attract $N_1$ and $N_2$ strongly but repel $N_3$
2. B.attract $N_1$ strongly, $N_2$ weakly and repel $N_3$ weakly
3. C.attract $N_1$ strongly, but repel $N_2$ and $N_3$ weakly
4. D.attract all three of them

In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a

1. A.helix
2. B.straight line
3. C.ellipse
4. D.circle

A long solenoid has 200 turns per $cm$ and carries a current $i$. The magnetic field at its center is $6.28\times 10^{-2}Weber/{\mathrm{m}}^2$. Another long solenoid has 100 turns per $cm$ and it carries a current $\frac{i}{3}$. The value of the magnetic field at its center is

1. A.$1.05\times 10^{-2}Weber/{\mathrm{m}}^2$
2. B.$1.05\times 10^{-5}Weber/{\mathrm{m}}^2$
3. C.$1.05\times 10^{-3}Weber/{\mathrm{m}}^2$
4. D.$1.05\times 10^{-4}Weber/{\mathrm{m}}^2$

A charged particle of mass $m$ and charge $q$ travels on a circular path of radius $r$ that is perpendicular to a magnetic field $B$. The time taken by the particle to complete one revolution is

1. A.$\frac{2\pi q^{2}B}{m}$
2. B.$\frac{2\pi mq}{B}$
3. C.$\frac{2\pi m}{qB}$
4. D.$\frac{2\pi qB}{m}$