Coulomb's Law

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JEE Main 2021

LEVELJEE Main

Two identical conducting spheres with negligible volume have $2.1 nC$ and $- 0.1 nC$ charges, respectively. They are brought into contact and then separated by a distance of $0.5 m$ . The electrostatic force acting between the spheres is ............... $\times 1 0^{- 9}$ N. [Given, $4 π ε_{0} = \frac{1}{9 \times 1 0 ^{9}}$ SI unit]

JEE Main 2021

LEVELJEE Main

An infinite number of point charges, each carrying $1 μ C$ charge, are placed along the Y-axis at $y = 1 m, 2 m, 4 m, 8 m \dots$ . The total force on a $1 C$ point charge, placed at the origin, is $x \times 1 0^{3} N$ . The value of $x$ to the nearest integer, is ............... . (Take, $\frac{1}{4 π ε _{0}} = 9 \times 1 0^{9} N-m^{2} / C^{2}$ )

JEE Main 2021

LEVELJEE Advanced

Two electrons each are fixed at a distance $2 d$ . A third charge proton placed at the mid-point is displaced slightly by a distance $x (x ≪ d)$ perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency? ( $m =$ mass of charged particle)

(A)

(\frac{2 q ^{2}}{π ε _{0} m d ^{3}})^{1/2}

(B)

(\frac{π ε _{0} m d ^{3}}{2 q ^{2}})^{1/2}

(C)

(\frac{q ^{2}}{2 π ε _{0} m d ^{3}})^{1/2}

(D)

(\frac{2 π ε _{0} m d ^{3}}{q ^{2}})^{1/2}

JEE Main 2021

LEVELJEE Advanced

A particle of mass $1 mg$ and charge $q$ is lying at the mid-point of two stationary particles kept at a distance $2 m$ when each is carrying same charge $q$ . If the free charged particle is displaced from its equilibrium position through distance $x$ ( $x ≪ 1 m$ ), the particle executes SHM. Its angular frequency of oscillation will be $\dots \times 1 0^{5} rad/s$ , if $q^{2} = 10 C^{2}$ .

LEVELJEE Advanced

Four charges equal to $- Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium, the value of $q$ is

(A)

- \frac{Q}{4} (1 + 22)

(B)

\frac{Q}{4} (1 + 22)

(C)

- \frac{Q}{2} (1 + 22)

(D)

\frac{Q}{2} (1 + 22)

JEE Main 2019

LEVELJEE Main

Three charges $+ Q, q, + Q$ are placed respectively at distance $0, d /2$ and $d$ from the origin on the X-axis. If the net force experienced by $+ Q$ placed at $x = 0$ is zero, then value of $q$ is

(A)

+ \frac{Q}{2}

(B)

+ \frac{Q}{4}

(C)

- \frac{Q}{2}

(D)

- \frac{Q}{4}

JEE Main 2013

LEVELJEE Advanced

Two charges each equal to $q$ , are kept at $x = - a$ and $x = a$ on the x-axis. A particle of mass $m$ and charge $q_{0} = q /2$ is placed at the origin. If charge $q_{0}$ is given, a small displacement ( $y << a$ ) along the y-axis, the net force acting on the particle is proportional to

(A)

y

(B)

- y

(C)

1/ y

(D)

- 1/ y

JEE Advanced 2014

LEVELJEE Main

Four charges $Q_{1}, Q_{2}, Q_{3}$ and $Q_{4}$ of same magnitude are fixed along the x-axis at $x = - 2 a, - a, + a$ and $+ 2 a$ respectively. A positive charge $q$ is placed on the positive y-axis at a distance $b > 0$ . Four options of the signs of these charges are given in Column I. The direction of the forces on the charge $q$ is given in Column II. Match Column I with Column II and select the correct answer using the code given below the lists. $\begin{array}{ll} \text{\textbf{Column I}} & \text{\textbf{Column II}} \\ \text{A. } Q_1, Q_2, Q_3, Q_4 \text{ all positive} & \text{p. } +x \\ \text{B. } Q_1, Q_2 \text{ positive; } Q_3, Q_4 \text{ negative} & \text{q. } -x \\ \text{C. } Q_1, Q_4 \text{ positive; } Q_2, Q_3 \text{ negative} & \text{r. } +y \\ \text{D. } Q_1, Q_3 \text{ positive; } Q_2, Q_4 \text{ negative} & \text{s. } -y \end{array}$

Two equal negative charges $- q$ are fixed at points $(0, - a)$ and $(0, a)$ on $y$ -axis. A positive charge $Q$ is released from rest at the point $(2 a, 0)$ on the $x$ -axis. The charge $Q$ will

(A)

execute simple harmonic motion about the origin

(B)

move to the origin and remain at rest

(C)

move to infinity

(D)

execute oscillatory but not simple harmonic motion

LEVELJEE Main

A charge $q$ is placed at the centre of the line joining two equal charges $Q$ . The system of the three charges will be in equilibrium if $q$ is equal to

(A)

- \frac{Q}{2}

(B)

- \frac{Q}{4}

(C)

+ \frac{Q}{4}

(D)

+ \frac{Q}{2}

LEVELJEE Advanced

Three particles, each of mass $1 g$ and carrying a charge $q$ , are suspended from a common point by insulated massless strings, each $100 cm$ long. If the particles are in equilibrium and are located at the corners of an equilateral triangle of side length $3 cm$ , calculate the charge $q$ on each particle. (Take $g = 10 m/s^{2}$ ).

JEE Advanced 2001

LEVELJEE Advanced

A small ball of mass $2 \times 1 0^{- 3} kg$ having a charge of $1 μ C$ is suspended by a string of length $0.8 m$ . Another identical ball having the same charge is kept at the point of suspension. Determine the minimum horizontal velocity which should be imparted to the lower ball, so that it can make complete revolution.

JEE Advanced 2014

LEVELJEE Advanced

Four charges $Q_{1}, Q_{2}, Q_{3}$ and $Q_{4}$ of same magnitude are fixed along the $x$ -axis at $x = - 2 a, - a, + a$ and $+ 2 a$ respectively. A positive charge $q$ is placed on the positive $y$ -axis at a distance $b > 0$ . Four options of the signs of these charges are given in Column I. The direction of the forces on the charge $q$ is given in Column II. Match Column I with Column II and select the correct answer using the code given below the lists.

List-I

(P)

Q_{1}, Q_{2}, Q_{3}, Q_{4}

all positive

(Q)

Q_{1}, Q_{2}

positive;

Q_{3}, Q_{4}

negative

(R)

Q_{1}, Q_{4}

positive;

Q_{2}, Q_{3}

negative

(S)

Q_{1}, Q_{3}

positive;

Q_{2}, Q_{4}

negative

List-II

(1)

+ x

(2)

- x

(3)

+ y

(4)

- y

LEVELJEE Main

Five point charges, each of value $+ q$ coulomb, are placed on five vertices of a regular hexagon of side $L$ metre. The magnitude of the force on the point charge of value $- q$ coulomb placed at the centre of the hexagon is ………newton.

LEVELJEE Main

Under the influence of the coulomb field of a fixed charge $+ Q$ , a charge $- q$ is moving around it in an elliptical orbit. Find out the correct statement(s).

(A)

The angular momentum of the charge

- q

is constant

(B)

The linear momentum of the charge

- q

is constant

(C)

The angular velocity of the charge

- q

is constant

(D)

The linear speed of the charge

- q

is constant

LEVELJEE Main

Two small balls having equal positive charges $Q$ (coulomb) on each are suspended by two insulating strings of equal length $L$ (metre) from a hook fixed to a stand. The whole setup is taken in a satellite into space where there is no gravity (state of weightlessness). The angle between the strings is ...... and the tension in each string is ...... newton.

JEE Advanced 2020

LEVELJEE Advanced

Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is $α$ . The spheres are now immersed in a dielectric liquid of density $800 kg m^{- 3}$ and dielectric constant $21$ . If the angle between the strings remains the same after the immersion, then

* Multiple Correct Options

(A)

electric force between the spheres remains unchanged

(B)

electric force between the spheres reduces

(C)

mass density of the spheres is

840 kg m^{- 3}

(D)

the tension in the strings holding the spheres remains unchanged

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Four charges equal to −Q are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium, the value of q is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to

List-I

List-II

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Under the influence of the coulomb field of a fixed charge +Q, a charge −q is moving around it in an elliptical orbit. Find out the correct statement(s).

Four charges equal to $- Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium, the value of $q$ is

A charge $q$ is placed at the centre of the line joining two equal charges $Q$ . The system of the three charges will be in equilibrium if $q$ is equal to

Under the influence of the coulomb field of a fixed charge $+ Q$ , a charge $- q$ is moving around it in an elliptical orbit. Find out the correct statement(s).