Question

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

JEE Main 2020 (02 Sep Shift 1)

Options

• A: $2 \mathrm{cm}$
• B: $5\mathrm{cm}$
• C: $12 \mathrm{cm}$
• D: $4 \mathrm{cm}$

Question

The figure shows a region of length '$\mathcal{l}$' with a uniform magnetic field of  $0.3 \mathrm{T}$ in it and a proton entering the region with velocity $4\times {10}^5 \mathrm{m} {\mathrm{s}}^{-1}$ making an angle $60°$ with the field. If the proton completes $10$ revolution by the time it cross the region shown, '$\mathcal{l}$' is close to (mass of proton $= 1.67\times {10}^{-27} \mathrm{kg}$, charge of the proton$= 1.6\times {10}^{-19} \mathrm{C}$)

JEE Main 2020 (02 Sep Shift 2)

Options

• A: $0.11 \mathrm{m}$
• B: $0.88 \mathrm{m}$
• C: $0.44 \mathrm{m}$
• D: $0.22 \mathrm{m}$

Question

A wire carrying current $\mathrm{I}$ is bent in the shape$\mathrm{ABCDEFA}$ as shown, where rectangle $\mathrm{ABCDA}$ and $\mathrm{ADEFA}$ are perpendicular to each other. If the sides of the rectangles are of lengths $\mathrm{a}$ and $\mathrm{b}$, then the magnitude and direction of magnetic moment of the loop $\mathrm{ABCDEFA}$ is :

JEE Main 2020 (02 Sep Shift 2)

Options

• A: $\sqrt{2}abI \mathrm{along} \left(\frac{{\displaystyle \hat{\mathrm{j}}}}{\sqrt{2}}+\frac{\hat{\mathrm{k}}}{\sqrt{2}}\right)$
• B: $abI$ along $\left(\frac{\hat{\mathrm{j}}}{\sqrt{2}}+\frac{\hat{\mathrm{k}}}{\sqrt{2}}\right)$
• C: $\sqrt{2}abI$ along $\left(\frac{\hat{\mathrm{j}}}{\sqrt{5}}+\frac{2\hat{\mathrm{k}}}{\sqrt{5}}\right)$
• D: $abI$ along $\left(\frac{\hat{\mathrm{j}}}{\sqrt{5}}+\frac{\hat{\mathrm{k}}}{\sqrt{5}}\right)$

Question

A wire $A$, bent in the shape of an arc of a circle, carrying a current of $2 \mathrm{A}$ and having radius $2 \mathrm{cm}$ and another wire $B$, also bent in the shape of an arc of a circle, carrying a current of $3 \mathrm{A}$ and having radius of $4\text{ cm}$, are placed as shown in the figure. The ratio of the magnetic fields due to the wires $\text{A}$ and $\text{B}$ at the common centre $\text{O}$ is:

JEE Main 2020 (04 Sep Shift 1)

Options

• A: $4:6$
• B: $6:4$
• C: $2:5$
• D: $6:5$

Question

A square loop of side $2a,$ and carrying current $I$ is kept in $XZ$ plane with its centre at origin. A long wire carrying the same current $I$ is placed parallel to the $z$-axis and passing through the point $(0, b, 0),(b>> a)$. The magnitude of the torque on the loop about $z$-axis is given by.

JEE Main 2020 (05 Sep Shift 1)

Options

• A: $\frac{{\mu }_0{I}^2{a}^2}{2\pi b}$
• B: $\frac{{\mu }_0{I}^2{a}^3}{2\pi b^2}$
• C: $\frac{2{\mu }_{0}I{}^{2}a^2}{\pi b}$
• D: $\frac{2{\mu }_{0}I{}^2\mathrm{a}^3}{\pi b^2}$

Question

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

JEE Main 2020 (07 Jan Shift 1)

Options

• A: Direction of $I_R$ remains unchanged and $V_R$ is maximum at $t=0.5$
• B: At $t=0.25$ direction of $I_R$ reverses and $V_R$ is maximum
• C: Direction of $I_R$ remains unchanged and $V_R$ is zero at $t=0.25$
• D: At $t=0.5$ direction of $I_R$ reverses and $V_R$ is zero

Question

An electron gun is placed inside a long solenoid of radius $R$ on its axis. The solenoid has $n$ turns/length and carries a current $I.$ The electron gun shoots an electron along the radius of the solenoid with speed $v.$ If the electron does not hit the surface of the solenoid, maximum possible value of $v$ is (all symbols have their standard meaning):

JEE Main 2020 (09 Jan Shift 2)

Options

• A: $\frac{e{\mu }_{0}nIR}{m}$
• B: $\frac{e{\mu }_{0}nIR}{2m}$
• C: $\frac{e{\mu }_{0}nIR}{4m}$
• D: $\frac{2e{\mu }_{0}nIR}{m}$

Question

The fractional change in the magnetic field intensity at a distance $r$ from centre on the axis of current carrying coil of radius $a$ to the magnetic field intensity at the centre of the same coil is: (Take $\mathrm{r}<\mathrm{a}$)

JEE Main 2021 (26 Aug Shift 1)

Options

• A: $\frac{2}{3}\frac{a^2}{r^2}$
• B: $\frac{3}{2}\frac{a^2}{r^2}$
• C: $\frac{3}{2}\frac{r^2}{a^2}$
• D: $\frac{2}{3}\frac{r^2}{a^2}$

Question

Figure $A$ and $B$ shown two long straight wires of circular cross-section ( $a$ and $b$ with $a<b$ ), carrying current $I$ which is uniformly distributed across the cross-section. The magnitude of magnetic field $B$ varies with radius $r$ and can be represented as:

JEE Main 2021 (27 Jul Shift 2)

Options

• A:
• B:
• C:
• D:

Question

A coil having $N$ turns is wound tightly in the form of a spiral with inner and outer radii $a$ and $b$ respectively. Find the magnetic field at centre, when a current $I$ passes through coil :

JEE Main 2021 (31 Aug Shift 1)

Options

• A: $\frac{{\mu }_{0}I}{8}\left[\frac{a+b}{a-b}\right]$
• B: $\frac{{\mu }_0\mathrm{I}}{4(\mathrm{a}-\mathrm{b})}\left[\frac{1}{\mathrm{a}}-\frac{1}{ \mathrm{b}}\right]$
• C: $\frac{{\mu }_{0}I}{8}\left(\frac{a-b}{a+b}\right)$
• D: $\frac{{\mu }_{0}IN}{2( b-a)}{\log }_e\left(\frac{b}{a}\right)$

Question

A long solenoid with $1000 \mathrm{turns} {\mathrm{m}}^{-1}$ has a core material with relative permeability $500$ and volume ${10}^3{ \mathrm{cm}}^3.$ If the core material is replaced by another material having relative permeability of $750$ with same volume maintaining same current of $0.75 \mathrm{A}$ in the solenoid, the fractional change in the magnetic moment of the core would be approximately $\left(\frac{x}{499}\right).$ Find the value of $x.$

JEE Main 2021 (31 Aug Shift 2)

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Question

Two concentric circular loops of radii $r_1=30 \mathrm{cm}$ and $r_2=50 \mathrm{cm}$ are placed in $X-Y$ plane as shown in the figure. A current $I=7 \mathrm{A}$ is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately

JEE Main 2022 (26 Jul Shift 2)

Options

• A: $\frac{7}{2}\hat{k} \mathrm{A} {\mathrm{m}}^2$
• B: $-\frac{7}{2}\hat{k} \mathrm{A} {\mathrm{m}}^2$
• C: $7\hat{k} \mathrm{A} {\mathrm{m}}^2$
• D: $-7\hat{k} \mathrm{A} {\mathrm{m}}^2$

Question

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 

JEE Main 2022 (26 Jun Shift 1)

Options

• A: $4:1$
• B: $2:1$
• C: $1:2$
• D: $1:4$

Question

Two long parallel conductors $S_1$ and $S_2$ are separated by a distance $10 \mathrm{cm}$ and carrying currents of $4 \mathrm{A}$ and $2 \mathrm{A}$ respectively. The conductors are placed along $x$-axis in $X-Y$ plane. There is a point $P$ located between the conductors (as shown in figure).
A charge particle of $3\pi$ coulomb is passing through the point $P$ with velocity $\overrightarrow{v}=\left(2\hat{i}+3\hat{j}\right) \mathrm{m} {\mathrm{s}}^{-1}$; where $\hat{i}$ & $\hat{j}$ represents unit vector along $x$ & $y$axis respectively.
The force acting on the charge particle is $4\pi \times {10}^{-5}\left(-x\hat{i}+2\hat{j}\right) \mathrm{N}$. The value of $x$ is 

JEE Main 2022 (27 Jun Shift 2)

Options

• A: $2$
• B: $1$
• C: $3$
• D: $-3$

Question

An infinitely long hollow conducting cylinder with radius $R$ carries a uniform current along its surface.

Choose the correct representation of magnetic field $\left(B\right)$as a function of radial distance $\left(r\right)$ from the axis of cylinder.

JEE Main 2022 (28 Jun Shift 1)

Options

• A:
• B:
• C:
• D:

Question

A deuteron and a proton moving with equal kinetic energy enter into to 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 _____ .

JEE Main 2022 (27 Jun Shift 2)

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Question

For a moving coil galvanometer, the deflection in the coil is $0.05 \mathrm{rad}$ when a current of $10 \mathrm{mA}$ is passed through it. If the torsional constant of suspension wire is $4.0 \times {10}^{–5} \mathrm{N} \mathrm{m} {\mathrm{rad}}^{-1}$, the magnetic field is $0.01 \mathrm{T}$ and the number of turns in the coil is $200$, the area of each turn (in ${\mathrm{cm}}^2$ ) is :

JEE Main 2023 (25 Jan Shift 2)

Options

• A: $2.0$
• B: $1.0$
• C: $1.5$
• D: $0.5$

Question

A long straight wire of circular cross-section (radius $a$) is carrying steady current $\mathrm{I}.$ The current $\mathrm{I}$ is uniformly distributed across this cross-section. The magnetic field is

JEE Main 2023 (06 Apr Shift 1)

Options

• A:

  inversely proportional to $r$ in the region $r<a$ and uniform throughout in the region $r>a$

• B:

  directly proportional to $r$ in the region $r<a$ and inversely proportional to $r$ in the region $r>a$

• C: Zero in the region $r<a$ and inversely proportional to $r$ in the region $r>a$
• D:

  uniform in the region $r<a$ and inversely proportional to distance $r$ from the axis, in the region $r>a$

Question

The magnetic field existing in a region is given by $\vec{B}=0.2(1+2 x) \hat{k} \mathrm{~T}$. A square loop of edge $50 \mathrm{~cm}$ carrying 0.5 A current is placed in $x-y$ plane with its edges parallel to the $x-y$ axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is_____ $\mathrm{mN}$.

JEE Main 2024 (04 Apr Shift 1)

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Question

Two parallel long current carrying wire separated by a distance $2 r$ are shown in the figure. The ratio of magnetic field at $A$ to the magnetic field produced at $C$ is $\frac{x}{7}$. The value of $x$ is _____

JEE Main 2024 (04 Apr Shift 2)

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Question

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 $m$ is _____.

JEE Main 2024 (05 Apr Shift 2)

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Question

A circular coil having 200 turns, $2.5 \times 10^{-4} \mathrm{~m}^2$ area and carrying $100 \mu \mathrm{A}$ current is placed in a uniform magnetic field of 1T. Initially the magnetic dipole moment $(\vec{M})$ was directed along $\vec{B}$. Amount of work, required to rotate the coil through $90^{\circ}$ from its initial orientation such that $\vec{M}$ becomes perpendicular to $\vec{B}$, is ______ $\mu \mathrm{J}$.

JEE Main 2024 (06 Apr Shift 1)

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Question

Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is $5.0 \mathrm{cm}$. The magnitude of the magnetic field at a point $\mathrm{P}$ midway between the wires is $\_\_\_\_\_ \mu \mathrm{T}$. (Given: ${\mu }_0=4\pi \times {10}^{-7} \mathrm{T} \mathrm{m} {\mathrm{A}}^{-1}$)

JEE Main 2024 (27 Jan Shift 1)

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Question

Two insulated circular loop $A$ and $B$ radius $a$ carrying a current of $I$ in the anti clockwise direction as shown in figure. The magnitude of the magnetic induction at the centre will be:

JEE Main 2024 (30 Jan Shift 1)

Options

• A: $\frac{\sqrt{2}{\mu }_{0}I}{a}$
• B: $\frac{{\mu }_{0}I}{2a}$
• C: $\frac{{\mu }_{0}I}{\sqrt{2}a}$
• D: $\frac{2{\mu }_{0}I}{a}$

Question

A regular polygon of $6$ sides is formed by bending a wire of length $4 \mathrm{\pi }$ meter. If an electric current of $4\pi \sqrt{3} \mathrm{A}$ is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x\times {10}^{-7} \mathrm{T}.$ The value of $x$ is ______.

JEE Main 2024 (01 Feb Shift 1)

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