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

The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to $1.2\times 10^{-5}$. What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?

1. A.$1.2\times 10^{-5}$
2. B.$1.2\times 10^{-3}$
3. C.$1.8\times 10^{-3}$
4. D.$2.4\times 10^{-5}$

A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be : (Assume the coil to be short circuited.)

1. A.Halved
2. B.Quadrupled
3. C.The same
4. D.Doubled

The susceptibility of a paramagnetic material is 99. The permeability of the material in $Wb/A\text{-}\mathrm{m}$, is : [Permeability of free space ${\mu }_0=4\pi \times 10^{-7}Wb/A\text{-}\mathrm{m}$]

1. A.$4\pi \times 10^{-7}$
2. B.$4\pi \times 10^{-4}$
3. C.$4\pi \times 10^{-5}$
4. D.$4\pi \times 10^{-6}$

A deuteron and a proton moving with equal kinetic energy enter into a uniform magnetic field at right angle to the field. If $r_d$ and $r_p$ are the radii of their circular paths respectively, then the ratio $\frac{r_d}{r_p}$ will be $\sqrt{x}:1$ where x is ________.

A metallic rod of length $20\text{ cm}$ is placed in North-South direction and is moved at a constant speed of $20\text{ m/s}$ towards East. The horizontal component of the Earth's magnetic field at that place is $4\times 10^{-3}\text{ T}$ and the angle of dip is $45^{\circ }$. The emf induced in the rod is ________ mV.

A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is :

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

A bar magnet having a magnetic moment of $2.0\times 10^5{\text{ JT}}^{-1}$, is placed along the direction of uniform magnetic field of magnitude $\mathrm{B}=14\times 10^{-5}\text{ T}$. The work done in rotating the magnet slowly through $60^{\circ }$ from the direction of field is :

1. A.14 J
2. B.8.4 J
3. C.4 J
4. D.1.4 J

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

1. A.$5\mu \text{V}$
2. B.$50\mu \text{V}$
3. C.5 mV
4. D.50 mV

A metal surface is illuminated by a radiation of wavelength $4500\text{A˚}$. The ejected photo-electron enters a constant magnetic field of 2 mT making an angle of $90^{\circ }$ with the magnetic field. If it starts revolving in a circular path of radius 2 mm, the work function of the metal is approximately :

1. A.1.36 eV
2. B.1.69 eV
3. C.2.78 eV
4. D.2.23 eV

A long straight wire with a circular cross-section having radius $\mathrm{R}$, is carrying a steady current $\mathrm{I}$. The current $\mathrm{I}$ is uniformly distributed across this cross-section. Then the variation of magnetic field due to current $\mathrm{I}$ with distance $r$ ($r<\mathrm{R}$) from its centre will be :

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

Given below are two statements : Statement I : Susceptibilities of paramagnetic and ferromagnetic substances increase with decrease in temperature. Statement II : Diamagnetism is a result of orbital motions of electrons developing magnetic moments opposite to the applied magnetic field. Choose the correct answer from the options given below :

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

A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to

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

A proton, a deuteron and an $\alpha$-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :

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

An electric bulb is rated as $200\mathrm{W}$. What will be the peak magnetic field at $4\mathrm{m}$ distance produced by the radiations coming from this bulb? Consider this bulb as a point source with $3.5\%$ efficiency.

1. A.$1.19\times 10^{-8}\mathrm{T}$
2. B.$1.71\times 10^{-8}\mathrm{T}$
3. C.$0.84\times 10^{-8}\mathrm{T}$
4. D.$3.36\times 10^{-8}\mathrm{T}$

A circular coil of 1000 turns each with area $1{\mathrm{m}}^2$ is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of $0.07\mathrm{T}$. The maximum voltage generation will be ____ $\mathrm{V}$.

1. A.(a), (c)
2. B.(a), (d)
3. C.(b), (d)
4. D.(b), (c)

1. A.$\frac{{\mu }_{0}I}{4\pi xy}\left[\sqrt{x^2+y^2}+(x+y)\right]$
2. B.$\frac{{\mu }_{0}I}{4\pi xy}\left[\sqrt{x^2+y^2}-(x+y)\right]$
3. C.$\frac{{\mu }_{0}Ixy}{4\pi }\left[\sqrt{x^2+y^2}-(x+y)\right]$
4. D.$\frac{{\mu }_{0}Ixy}{4\pi }\left[\sqrt{x^2+y^2}+(x+y)\right]$

A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of $50{\text{ rad s}}^{-1}$ in a uniform horizontal magnetic field of $3.0\times 10^{-2}\text{ T}$. The maximum emf induced the coil will be ............... $\times 10^{-2}\text{ volt}$ (rounded off to the nearest integer)

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

The value of aluminium susceptibility is $2.2\times 10^{-5}$. The percentage increase in the magnetic field if space within a current carrying toroid is filled with aluminium is $\frac{x}{10^4}$. Then the value of x is ____.

Two ions having same mass have charges in the ratio 1 : 2. They are projected normally in a uniform magnetic field with their speeds in the ratio 2 : 3. The ratio of the radii of their circular trajectories is :

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

A light beam of wavelength 500 nm is incident on a metal having work function of 1.25 eV, placed in a magnetic field of intensity B. The electrons emitted perpendicular to the magnetic field B, with maximum kinetic energy are bent into circular arc of radius 30 cm. The value of B is ____ $\times 10^{-7}$ T. Given hc = $20\times 10^{-26}$ J-m, mass of electron = $9\times 10^{-31}$ kg

Intensity of sunlight is observed as $0.092{\text{ Wm}}^{-2}$ at a point in free space. What will be the peak value of magnetic field at the point? (${\epsilon }_0=8.85\times 10^{-12}{\text{ C}}^2{\text{N}}^{-1}{\text{m}}^{-2}$)

1. A.$2.77\times 10^{-8}\text{ T}$
2. B.$1.96\times 10^{-8}\text{ T}$
3. C.$8.31\text{ T}$
4. D.$5.88\text{ T}$

Statement I : The ferromagnetic property depends on temperature. At high temperature, ferromagnet becomes paramagnet. Statement II : At high temperature, the domain wall area of a ferromagnetic substance increases. In the light of the above statements, choose the most appropriate answer from the options given below :

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

A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let $r_d$ and $r_{\alpha }$ be their respective radii of circular path. The value of $\frac{r_d}{r_{\alpha }}$ is equal to :

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