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

1. A.$48\mu \mathrm{V}$
2. B.$28\mu \mathrm{V}$
3. C.$56\mu \mathrm{V}$
4. D.$36\mu \mathrm{V}$

1. A.$\frac{{\mu }_{0}I}{2\pi R}(\pi +1)$
2. B.$\frac{{\mu }_{0}I}{2\pi R}\left(\pi -\frac{1}{\sqrt{2}}\right)$
3. C.$\frac{{\mu }_{0}I}{2R}$
4. D.$\frac{{\mu }_{0}I}{2\pi R}\left(\pi +\frac{1}{\sqrt{2}}\right)$

A long solenoid of radius R carries a time (t) - dependent current $I(t)=I_{0}t(1-t)$. A ring of radius 2R is placed coaxially near its middle. During the time interval $0\le t\le 1$, the induced current ($I_R$) and the induced EMF($V_R$) in the ring change as :

1. A.Direction of $I_R$ remains unchanged and $V_R$ is zero at t = 0.25
2. B.Direction of $I_R$ remains unchanged and $V_R$ is maximum at t = 0.5
3. C.At t = 0.25 direction of $I_R$ reverses and $V_R$ is maximum
4. D.At t = 0.5 direction of $I_R$ reverses and $V_R$ is zero

A loop ABCDEFA of straight edges has six corner points $\mathrm{A}(0,0,0)$, $\mathrm{B}(5,0,0)$, $\mathrm{C}(5,5,0)$, $\mathrm{D}(0,5,0)$, $\mathrm{E}(0,5,5)$ and $\mathrm{F}(0,0,5)$. The magnetic field in this region is $\vec{B}=(3\hat{i}+4\hat{k})T$. The quantity of flux through the loop ABCDEFA (in Wb) is ____.

A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at :

1. A.2.5 s and 7.5 s
2. B.5.0 s and 10.0 s
3. C.5.0 s and 7.5 s
4. D.2.5 s and 5.0 s

1. A.1.0 T, 50A/m and 1.5 T
2. B.1.5 T, 50 A/m and 1.0 T
3. C.1.5 T, 50 A/m and 2.0 T
4. D.150 A/m, 1.0 T and 1.5 T

A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of $40\pi {\text{ rad s}}^{-1}$ about its axis, perpendicular to its plane. If the magnetic field at its centre is $3.8\times 10^{-9}\text{ T}$, then the charge carried by the ring is close to (${\mu }_0=4\pi \times 10^{-7}{\text{ N/A}}^2$).

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

A magnetic compass needle oscillates 30 times per minute at a place where the dip is $45^{\circ }$, and 40 times per minute where the dip is $30^{\circ }$. If $B_1$ and $B_2$ are respectively the total magnetic field due to the earth at the two places, then the ratio $\frac{B_1}{B_2}$ is best given by :

1. A.1.8
2. B.2.2
3. C.0.7
4. D.3.6

1. A.2.25 cm
2. B.12.87 cm
3. C.1.22 cm
4. D.11.65 cm

1. A.$1.5\times 10^{-5}\text{ T}$
2. B.$3.0\times 10^{-5}\text{ T}$
3. C.$2.0\times 10^{-5}\text{ T}$
4. D.$2.5\times 10^{-5}\text{ T}$

A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicualr to the plane. Let ${\mathrm{r}}_{\mathrm{p}}$, ${\mathrm{r}}_{\mathrm{e}}$ and ${\mathrm{r}}_{\mathrm{He}}$ be their respective radii, then

1. A.${\mathrm{r}}_{\mathrm{e}}<{\mathrm{r}}_{\mathrm{p}}<{\mathrm{r}}_{\mathrm{He}}$
2. B.${\mathrm{r}}_{\mathrm{e}}<{\mathrm{r}}_{\mathrm{p}}={\mathrm{r}}_{\mathrm{He}}$
3. C.${\mathrm{r}}_{\mathrm{e}}>{\mathrm{r}}_{\mathrm{p}}>{\mathrm{r}}_{\mathrm{He}}$
4. D.${\mathrm{r}}_{\mathrm{e}}>{\mathrm{r}}_{\mathrm{p}}={\mathrm{r}}_{\mathrm{He}}$

The magnitude of the magnetic field at the centre of an equilateral triangular loop of side 1 m which is carrying a current of 10 A is : [Take ${\mu }_0=4\pi \times 10^{-7}\mathrm{N}{\mathrm{A}}^{-2}$]

1. A.$3\mu \mathrm{T}$
2. B.$18\mu \mathrm{T}$
3. C.$9\mu \mathrm{T}$
4. D.$1\mu \mathrm{T}$

The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to :

1. A.$1/L^2$
2. B.1/L
3. C.L
4. D.$L^2$

The magnetic field of a plane electromagnetic wave is given by : $$\vec{B}=B_0\hat{i}[\cos (kz-\omega t)]+B_i\hat{j}\cos (kz+\omega t)$$ $B_0=3\times 10^{-5}\mathrm{T}$ and B1 = $2\times 10^{-6}\mathrm{T}$. The rms value of the force experienced by a stationary charge $Q=10^{-4}\mathrm{C}$ at z = 0 is closest to :

1. A.0.6 N
2. B.0.9 N
3. C.$3\times 10^{-2}\mathrm{N}$
4. D.0.1 N

A moving coil galvanometer has a coil with 175 turns and area $1\mathrm{c}{\mathrm{m}}^2$. It uses a torsion band of torsion constant $10^{-6}\mathrm{N}\text{-}m/rad$. The coil is placed in a maganetic field B parallel to its plane. The coil deflects by $1^{\circ }$ for a current of 1 mA. The value of B (in Tesla) is approximately :-

1. A.$10^{-4}$
2. B.$10^{-2}$
3. C.$10^{-1}$
4. D.$10^{-3}$

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

1. A.$+\frac{{\mu }_{0}I}{\pi d}(\hat{z})$
2. B.$-\frac{{\mu }_{0}I}{2\pi d}(\hat{x}+\hat{y})$
3. C.Zero
4. D.$\frac{{\mu }_{0}I}{2\pi d}(\hat{x}+\hat{y})$

1. A.$40\mathrm{A}$, perpendicular into the page
2. B.$40\mathrm{A}$, perpendicular out of the page
3. C.$20\mathrm{A}$, perpendicular into the page
4. D.$20\mathrm{A}$, perpendicular out of the page

A proton and an $\alpha$-particle (with their masses in the ratio of $1:4$ and charges in the ratio of $1:2$) are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii $r_p:r_{\alpha }$ of the circular paths described by them will be ;

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

The mean intensity of radiation on the surface of the Sun is about $10^{8}W/{\mathrm{m}}^2$ . The rms value of the corresponding magnetic field is closet to :

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

A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of $5.0\mathrm{m}{\mathrm{s}}^{-1}$, at right angles to the horizontal component of the earth's magnetic field of $0.3\times 10^{-4}Wb/{\mathrm{m}}^2$. The value of the induced emf in wire is :

1. A.$0.3\times 10^{-3}\mathrm{V}$
2. B.$2.5\times 10^{-3}\mathrm{V}$
3. C.$1.5\times 10^{-3}\mathrm{V}$
4. D.$1.1\times 10^{-3}\mathrm{V}$

A paramagnetic material has $10^{28}atoms/{\mathrm{m}}^3$. Its magnetic susceptibility at temperature 350 K is $2.8\times 10^{-4}$. Its susceptibility at 300 K is :

1. A.$3.726\times 10^{-4}$
2. B.$2.672\times 10^{-4}$
3. C.$3.672\times 10^{-4}$
4. D.$3.267\times 10^{-4}$

The region between $y=0$ and $y=d$ contains a magnetic field $\vec{B}=B\hat{z}$. A particle of mass m and charge q enters the region with a velocity $\vec{v}=v\hat{i}$. If $d=\frac{mv}{2qB}$, the acceleration of the charged particle at the point of its emergence at the other side is :

1. A.$\frac{qvB}{m}\left(-\frac{\sqrt{3}}{2}\hat{i}-\frac{1}{2}\hat{j}\right)$
2. B.$\frac{qvB}{m}\left(\frac{1}{2}\hat{i}-\frac{\sqrt{3}}{2}\hat{j}\right)$
3. C.$\frac{qvB}{m}\left(\frac{-\hat{j}+\hat{i}}{\sqrt{2}}\right)$
4. D.$\frac{qvB}{m}\left(\frac{\hat{j}+\hat{i}}{\sqrt{2}}\right)$

A particle of mass m and charge q is in an electric and magnetic field given by $$\vec{E}=2\hat{i}+3\hat{j};\vec{B}=4\hat{j}+6\hat{k}.$$ The charged particle is shifted from the origin to the point $\mathrm{P}(x=1;y=1)$ along a straight path. The magnitude of the total work done is :

1. A.(2.5) q
2. B.(0.35) q
3. C.(0.15) q
4. D.5 q

1. A.$1.0\times 10^{-7}\text{ T}$
2. B.$1.5\times 10^{-7}\text{ T}$
3. C.$1.5\times 10^{-5}\text{ T}$
4. D.$1.0\times 10^{-5}\text{ T}$