Question

Consider the force $\mathrm{F}$ on a charge '$\mathrm{q}$' due to a uniformly charged spherical shell of radius $\mathrm{R}$ carrying charge $\mathrm{Q}$ distributed uniformly over it. Which one of the following statements is true for $\mathrm{F}$, if  '$\mathrm{q}$' is placed at distance $\mathrm{r}$ from the centre of the shell?

JEE Main 2020 (06 Sep Shift 2)

Options

• A: $\mathrm{F}=\frac{1}{4\mathrm{\pi }{\in }_0}\frac{\mathrm{Qq}}{{\mathrm{R}}^2}$ for $\mathrm{r}<\mathrm{R}$
• B: $\frac{1}{4\mathrm{\pi }{\in }_0}\frac{\mathrm{qQ}}{{\mathrm{R}}^2}>\mathrm{F}>0$ for $\mathrm{r}<\mathrm{R}$
• C: $\mathrm{F}=\frac{1}{4\mathrm{\pi }{\in }_0}\frac{\mathrm{Qq}}{{\mathrm{r}}^2}$ for $\mathrm{r}>\mathrm{R}$
• D: $\mathrm{F}=\frac{1}{4\mathrm{\pi }{\in }_0}\frac{\mathrm{Qq}}{{\mathrm{r}}^2}$ for all $\mathrm{r}$

Question

In finding the electric field using Gauss law the formula $\left|\overrightarrow{E}\right|=\frac{q_{\mathrm{e}\mathrm{n}\mathrm{c}}}{{\epsilon }_0\left|A\right|}$ is applicable. In the formula ${\epsilon }_0$ is permittivity of free space, $A$ is the area of Gaussian surface and $q_{\mathrm{e}\mathrm{n}\mathrm{c}}$ is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation?

JEE Main 2020 (08 Jan Shift 1)

Options

• A: Only when the Gaussian surface is an equipotential surface
• B: Only when the Gaussian surface is an equipotential surface and $\left|\overrightarrow{E}\right|$ is constant on the surface.
• C: Only when $\left|\overrightarrow{E}\right|=$ constant on the surface.
• D: For any choice of Gaussian surface.

Question

A cube is placed inside an electric field, $\overrightarrow{E}=150y^2\hat{\mathrm{j}}$ The side of the cube is $0.5 \mathrm{m}$ and is placed in the field as shown in the given figure. The charge inside the cube is:

JEE Main 2021 (01 Sep Shift 2)

Options

• A: $8.3\times {10}^{-11}\mathrm{C}$
• B: $3.8\times {10}^{-11}\mathrm{C}$
• C: $3.8\times {10}^{-12}\mathrm{C}$
• D: $8.3\times {10}^{-12}\mathrm{C}$

Question

A cube of side $a$ has point charges $+\mathrm{Q}$ located at each of its vertices except at the origin where the charge is $-\mathrm{Q}.$ The electric field at the centre of cube is:

JEE Main 2021 (24 Feb Shift 1)

Options

• A: $\frac{-Q}{3\sqrt{3}\pi {\epsilon }_0{a}^2}\left(\hat{x}+\hat{y}+\hat{z}\right)$
• B: $\frac{Q}{3\sqrt{3}\pi {\epsilon }_0{a}^2}\left(\hat{x}+\hat{y}+\hat{z}\right)$
• C: $\frac{-2Q}{3\sqrt{3}\pi {\epsilon }_0{a}^2}\left(\hat{x}+\hat{y}+\hat{z}\right)$
• D: $\frac{2Q}{3\sqrt{3}\pi {\epsilon }_0{a}^2}\left(\hat{x}+\hat{y}+\hat{z}\right)$

Question

Two ideal electric dipoles $A$ and $B$, having their dipole moment $p_1$ and $p_2$ respectively are placed on a plane with their centres at $O$ as shown in the figure. At point $C$ on the axis of dipole $A$, the resultant electric field is making an angle of $37°$ with the axis. The ratio of the dipole moment of $A$ and $B,\frac{p_1}{p_2}$ is$:($ take $\left.\sin 37°=\frac{3}{5}\right)$

JEE Main 2021 (25 Jul Shift 2)

Options

• A: $\frac{3}{8}$
• B: $\frac{3}{2}$
• C: $\frac{2}{3}$
• D: $\frac{4}{3}$

Question

A solid metal sphere of radius $R$ having charge $q$ is enclosed inside the concentric spherical shell of inner radius $a$ and outer radius $b$ as shown in the figure. The approximate variation electric field $\overrightarrow{E}$, as a function of distance $r$, from centre $O$, is given by:

JEE Main 2021 (26 Aug Shift 1)

Options

• A:
• B:
• C:
• D:

Question

The electric field in a region is given by $\overrightarrow{E}=\left(\frac{3}{5}{E}_0\hat{\mathrm{i}}+\frac{4}{5}{E}_0\hat{\mathrm{j}}\right) \mathrm{N} {\mathrm{C}}^{-1}$. The ratio of flux of reported field through the rectangular surface of area $0.2 {\mathrm{m}}^2$ (parallel to $y-z$ plane) to that of the surface of area $0.3 {\mathrm{m}}^2$ (parallel to $x-z$ plane) is $a:b=a:2,$ where $a=?$ [Here $\hat{\mathrm{i}}, \hat{\mathrm{j}}$ and $\hat{\mathrm{k}}$ are unit vectors along $x, y$ and $z$ -axes respectively]

JEE Main 2021 (25 Feb Shift 1)

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Question

Two identical conducting spheres with negligible volume have $2.1 \mathrm{nC}$ and $-0.1 \mathrm{nC}$ charges, respectively. They are brought into contact and then separated by a distance of $0.5 \mathrm{m}$. The electrostatic force acting between the spheres is ___$\times {10}^{-9} \mathrm{N}$.
[Given : $4\pi {\epsilon }_0=\frac{1}{9\times {10}^9}$ SI unit]

JEE Main 2021 (25 Feb Shift 2)

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Question

A long cylindrical volume contains a uniformly distributed charge of density $\rho$. The radius of cylindrical volume is $R$. A charge particle $\left(q\right)$ revolves around the cylinder in a circular path. The kinetic energy of the particle is :

JEE Main 2022 (24 Jun Shift 2)

Options

• A: $\frac{\rho q{R}^2}{4{\epsilon }_o}$
• B: $\frac{\rho q{R}^2}{2{\epsilon }_o}$
• C: $\frac{q\rho }{4{\epsilon }_0{R}^2}$
• D: $\frac{4{\epsilon }_0{R}^2}{q\rho }$

Question

Sixty four conducting drops each of radius $0.02 \mathrm{m}$ and each carrying a charge of $5 \mu \mathrm{C}$ are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be

JEE Main 2022 (26 Jun Shift 2)

Options

• A: $1:4$
• B: $4:1$
• C: $1:8$
• D: $8:1$

Question

Two identical positive charges $Q$ each are fixed at a distance of $2a$ apart from each other. Another point charge $q_0$ with mass $m$ is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $q_0$ executes SHM. The time period of oscillation of charge $q_0$ will be

JEE Main 2022 (27 Jul Shift 1)

Options

• A: $\sqrt{\frac{4{\pi }^3{\epsilon }_{0}m{a}^3}{q_{0}Q}}$
• B: $\sqrt{\frac{q_{0}Q}{4{\pi }^3{\epsilon }_{0}m{a}^3}}$
• C: $\sqrt{\frac{2{\pi }^2{\epsilon }_{0}m{a}^3}{q_{0}Q}}$
• D: $\sqrt{\frac{8{\pi }^3{\epsilon }_{0}m{a}^3}{q_{0}Q}}$

Question

If a charge $q$ is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be

JEE Main 2022 (27 Jun Shift 2)

Options

• A: $\frac{q}{{\epsilon }_0}$
• B: $\frac{q}{2{\epsilon }_0}$
• C: $\frac{\mathrm{q}}{4{\epsilon }_0}$
• D: $\frac{q}{2\pi {\epsilon }_0}$

Question

A spherically symmetric charge distribution is considered with charge density varying as

$\rho \left(r\right)=\left\{\begin{array}{ll}{\rho }_0\left(\frac{3}{4}-\frac{r}{R}\right)& \text{ for }r\le R\\ \mathrm{Zero}& & & \mathrm{for} r>R\end{array}\right.$

Where, $r\left(r<R\right)$ is the distance from the centre $O$ (as shown in figure). The electric field at point $P$ will be :

JEE Main 2022 (29 Jul Shift 1)

Options

• A: $\frac{{\rho }_{0}r}{4{\epsilon }_0}\left(\frac{3}{4}-\frac{r}{R}\right)$
• B: $\frac{{\rho }_{0}r}{3{\epsilon }_0}\left(\frac{3}{4}-\frac{r}{R}\right)$
• C: $\frac{{\rho }_{0}r}{4{\epsilon }_0}\left(1-\frac{r}{R}\right)$
• D: $\frac{{\rho }_{0}r}{5{\epsilon }_0}\left(1-\frac{r}{R}\right)$

Question

Two identical metallic spheres $A$ and $B$ when placed at certain distance in air repel each other with a force of $F$. Another identical uncharged sphere $C$ is first placed in contact with $A$ and then in contact with $B$ and finally placed at midpoint between spheres $A$and $B$. The force experienced by sphere $C$ will be :

JEE Main 2022 (29 Jul Shift 2)

Options

• A: $\frac{3F}{2}$
• B: $\frac{3F}{4}$
• C: $F$
• D: $2F$

Question

If the electric potential at any point $\left(x, y, z\right) \mathrm{m}$ in space is given by $V=3x^2$ volt. The electric field at the point $\left(1, 0, 3\right) \mathrm{m}$ will be :

JEE Main 2022 (29 Jun Shift 2)

Options

• A: $3 {\mathrm{Vm}}^{-1}$, directed along positive $x$-axis.
• B: $3 {\mathrm{Vm}}^{-1}$, directed along negative $x$-axis.
• C: $6 {\mathrm{Vm}}^{-1}$, directed along negative $x$-axis.
• D: $6 {\mathrm{Vm}}^{-1}$, directed along positive $x$-axis.

Question

A $1 \mathrm{m}$ long copper wire carries a current of $1 \mathrm{A}$. If the cross section of the wire is $2.0{ \mathrm{mm}}^2$ and the resistivity of copper is $1.7\times {10}^{-8} \mathrm{\Omega } \mathrm{m}$. The force experienced by moving electron in the wire is _____$\times {10}^{-23} \mathrm{N}$

(Charge of electron$=1.6\times {10}^{-19}\mathrm{C}$ )

JEE Main 2022 (27 Jul Shift 1)

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Question

A dipole comprises of two charged particles of identical magnitude $q$ and opposite in nature. The mass $m$ of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance $l$ . If the dipole is placed in a uniform electric field $\overrightarrow{E}$; in such a way that dipole axis makes a very small angle with the electric field, $\overrightarrow{E}$. The angular frequency of the oscillations of the dipole when released is given by:

JEE Main 2023 (06 Apr Shift 2)

Options

• A: $\sqrt{\frac{3qE}{2ml}}$
• B: $\sqrt{\frac{8qE}{ml}}$
• C: $\sqrt{\frac{4qE}{ml}}$
• D: $\sqrt{\frac{8qE}{3ml}}$

Question

An electron revolves around an infinite cylindrical wire having uniform linear charge density $2\times {10}^{-8}$ $\mathrm{C} {\mathrm{m}}^{-1}$ in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is ______________ $\times {10}^6 \mathrm{m} {\mathrm{s}}^{-1}$. Given mass of electron $=9\times {10}^{-31} \mathrm{kg}$

JEE Main 2023 (10 Apr Shift 2)

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Question

An infinitely long positively charged straight thread has a linear charge density $\lambda \mathrm{Cm}^{-1}$. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is :

JEE Main 2024 (04 Apr Shift 1)

Options

• A:
  
• B:
  
• C:
  
• D:
  

Question

An infinite plane sheet of charge having uniform surface charge density $+\sigma_s \mathrm{C} / \mathrm{m}^2$ is placed on $x-y$ plane. Another infinitely long line charge having uniform linear charge density $+\lambda_e \mathrm{C} / \mathrm{m}$ is placed at $z=4 \mathrm{~m}$ plane and parallel to $y$-axis. If the magnitude values $\left|\sigma_{\mathrm{s}}\right|=2\left|\lambda_{\mathrm{e}}\right|$ then at point $(0,0,2)$, the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $\pi \sqrt{n}: 1$. The value of $n$ is_______.

JEE Main 2024 (04 Apr Shift 1)

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Question

Two identical conducting spheres $P$ and $S$ with charge $Q$ on each, repel each other with a force $16 \mathrm{~N}$. A third identical uncharged conducting sphere $R$ is successively brought in contact with the two spheres. The new force of repulsion between $\mathrm{P}$ and $\mathrm{S}$ is :

JEE Main 2024 (06 Apr Shift 2)

Options

• A: $1 \mathrm{~N}$
• B: $6 \mathrm{~N}$
• C: $12 \mathrm{~N}$
• D: $4 \mathrm{~N}$

Question

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $S$ having surface charge density $+\sigma$. The electron at $t=0$ is at a distance of $1 \mathrm{m}$ from $S$ and has a speed of $1 \mathrm{m} {\mathrm{s}}^{-1}$. The maximum value of $\sigma$, if the electron strikes $S$ at $t=1 \mathrm{s}$ is $\alpha \left[\frac{m{ϵ}_0}{e}\right] \frac{\mathrm{C}}{{\mathrm{m}}^2}$. The value of $\alpha$ is _____.

JEE Main 2024 (29 Jan Shift 1)

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Question

Two identical charged spheres are suspended by strings of equal lengths. The string make an angle of $37°$ with each other. When suspended in a liquid of density $0.7 \mathrm{g} {\mathrm{cm}}^{-3}$, the angle remains same. If density of material of the sphere is $1.4 \mathrm{g} {\mathrm{cm}}^{-3}$, the dielectric constant of the liquid is _____ $\left(\tan 37°=\frac{3}{4}\right)$

JEE Main 2024 (30 Jan Shift 2)

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Question

A thin metallic wire having cross sectional area of ${10}^{-4} {\mathrm{m}}^2$ is used to make a ring of radius $30 \mathrm{cm}$. A positive charge of $2\pi \mathrm{C}$ is uniformly distributed over the ring, while another positive charge of $30 \mathrm{pC}$ is kept at the centre of the ring. The tension in the ring is $\mathrm{\_\_\_\_\_\_\_} \mathrm{N}$; provided that the ring does not get deformed (neglect the influence of gravity).

(Given, $\frac{1}{4\pi {ϵ}_0}=9\times {10}^9$ SI units)

JEE Main 2024 (27 Jan Shift 1)

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