Electric Charges and Fields

The force between two point charges $q$ and $-q$ is $F$ at distance $r$. If the charges are changed to $2q$ and $-2q$ and the distance is doubled, the force will be:

Two charges are separated by distance $r$. If a glass slab is placed between them, the force between the charges will:

Which fundamental interaction is responsible for the stability of an atom by keeping electrons bound to the nucleus?

If two point charges are $q_1 = +3\mu\text{C}$ and $q_2 = +5\mu\text{C}$, the ratio of the force $\vec{F}_{12}$ to $\vec{F}_{21}$ in terms of magnitude is:

Two charges $+Q$ and $-Q$ are kept at points $A$ and $B$ respectively. A third charge $q$ is placed at the midpoint $C$ of $AB$. The net force on $q$ is:

Which of the following graphs best represents the variation of force $F$ between two point charges with the reciprocal of the square of the distance ($1/r^2$) between them?

Two point charges $q$ and $4q$ are $12 cm$ apart. Where should a third charge $Q$ be placed so that the system is in equilibrium?

Two charges $+Q$ and $-Q$ are kept at points $A$ and $B$ respectively. A third charge $q$ is placed at the midpoint of $AB$. If this charge $q$ is slightly displaced along the perpendicular bisector of $AB$, then:

Three charges $+4q, Q, +q$ are placed in a straight line of length $l$ at points $0, l/2, l$ respectively. What should be $Q$ in order to make the net force on $+q$ zero?

Suppose the charge of an electron and a proton vary slightly such that the net charge on a hydrogen atom is $\Delta q = e_{proton} + e_{electron} \neq 0$. If the net force (gravitational + electrostatic) between two hydrogen atoms at a distance $d$ is zero, then $\Delta q$ is of the order of (Mass of hydrogen atom $M = 1.67 \times 10^{-27} \text{ kg}$):

What is the direction of the electric field at the center of a dipole?

Electric field lines are used to visualize:

According to the principle of superposition, the net electric field at a point due to multiple charges is the ________ of individual fields.

The electric field at a point is $E$. If the charge creating the field is doubled and the distance is also doubled, the new electric field will be:

Two infinite parallel planes have surface charge densities $+\sigma$ and $+\sigma$. The electric field in the region between the planes is:

A soap bubble is given a negative charge. Its radius will:

For a point charge, the equipotential surfaces are:

Two point charges $+q_1$ and $-q_2$ ($q_1 > q_2 > 0$) are placed at a distance $d$ apart in vacuum. An electric field line emanates from the positive charge $+q_1$ at an angle $\alpha$ relative to the line segment connecting the two charges. For this field line to eventually terminate on the negative charge $-q_2$, what is the maximum permissible value of the angle $\alpha$?

Two point charges $Q$ and $-Q/4$ are separated by a distance $L$. The location of the point where the net electric field is zero is:

A charged particle is balanced in air by a vertical electric field $E$. If the direction of the field is reversed, the acceleration of the particle (neglecting air resistance) is:

What is the flux through a disk of radius $r$ when it is tilted such that its normal makes an angle of $90^\circ$ with a uniform electric field $E$?

The electric flux through a closed surface depends only on the __________ charge.

If a dielectric medium of constant $K$ is filled inside a closed surface enclosing a charge $q$, the net flux becomes:

Which of the following describes the relationship between the total flux and the number of electric field lines?

A point charge $q$ is placed at a distance $d$ from the center of a flat disk of radius $R$. If the flux through the disk is $q/4\epsilon_0$, what is the relationship between $R$ and $d$?

The net flux through a closed surface containing a charge $q$ is $\Phi$. If a dielectric slab is now placed inside the surface, the new net flux is:

A cube of side $a$ is placed in a uniform electric field $\vec{E} = E_0 \hat{i}$. What is the flux through the faces parallel to the $x-z$ plane?

In a region where the electric field is $\vec{E} = E_0 x \hat{i}$, the flux through a sphere of radius $R$ centered at the origin is:

A charge $q$ is placed at the center of a circular area. The flux through the area is:

A solid sphere of radius $R$ has a charge $Q$ distributed such that the density $\rho = kr$. The flux through a concentric sphere of radius $R/2$ is:

The Gaussian surface for a charged infinite plane sheet is usually taken as a:

What is the net flux through a closed surface if it encloses three charges: $+5q, -2q,$ and $-3q$?

When applying Gauss's Law to a point charge, the electric field is assumed to be:

The constant $\epsilon_0$ in Gauss's Law is called:

In a region of space, the electric field is $\vec{E} = E_0 x \hat{i}$. The net charge inside a cube of side $a$ with one corner at the origin and edges along the axes is:

A Gaussian surface encloses an object with a net charge of $-1.0$ nC. If the flux through the surface is measured to be $-113$ N m$^2$/C, what is the value of $\epsilon_0$ used in this calculation?

An electric dipole of length 2 cm is placed with its axis making an angle of 30 degrees to a uniform electric field $10^5$ N/C. If it experiences a torque of $10\sqrt{3}$ Nm, then the charge on the dipole is:

A large non-conducting sheet of thickness $t$ has a uniform charge density $\rho$. The electric field at a distance $r > t/2$ from the center of the sheet is:

An infinite slab of thickness $2d$ (from $x = -d$ to $x = +d$) has a uniform volume charge density $\rho$. The electric field at a point $x$ ($|x| < d$) is:

A point charge $q$ is placed at the vertex of a cone of semi-vertical angle $\theta$ and slant height $L$. The flux through the base of the cone is:

Which of the following statements about charge is FALSE?

What happens to the leaves of a gold leaf electroscope when a charged body touches the metal disk?

The property of 'additivity of charges' follows which law of addition?

In a conductor, the electric charge resides:

Three identical metal spheres $P$, $Q$, and $R$ are mounted on insulating stands. Sphere $P$ has an initial charge of $+12 \mu\text{C}$, while $Q$ and $R$ are initially uncharged. The spheres are brought into contact in the following sequence: first $P$ is touched to $Q$ and separated, then $Q$ is touched to $R$ and separated, and finally $P$ is touched to $R$ and separated. What is the final charge on sphere $R$?

Two identical neutral conducting spheres, $X$ and $Y$, are in contact with each other and supported on insulating stands. A positively charged glass rod is brought near sphere $X$. While the rod is still held near $X$, sphere $Y$ is moved away using its insulating handle. Finally, the glass rod is removed. What are the final charges on spheres $X$ and $Y$?

Which of the following is the best way to determine if an object is definitely charged?

If a negatively charged rod is held near a neutral metal ball, the net force on the ball is:

When a conductor is grounded, the earth acts as:

Two pith balls carrying equal charges are suspended from a common point by strings of equal length. The equilibrium separation between them is $r$. If the strings are rigidly clamped at half the height, the equilibrium separation between the balls now becomes:

The net force on a charge $q$ due to a distribution of charges is the vector sum of individual forces. This is a consequence of the _______ nature of the electric field.

Which of the following is NOT a property of the force between multiple charges?

The ratio of electrostatic force to gravitational force between two protons is of the order of:

If a charge $q$ is placed at the center of the line joining two equal charges $Q$, the system of three charges will be in equilibrium if $q$ is equal to:

Which of the following is the correct vector form of the force $\vec{F_{12}}$ exerted by charge $q_1$ on $q_2$?

Two point charges $Q$ and $-3Q$ are placed at some distance apart. If the electric field at the location of $Q$ is $E$, then the electric field at the location of $-3Q$ is:

Three charges $+q, +2q$ and $+4q$ are connected by two strings of length $L$ each in a straight line. What is the ratio of tensions $T_1/T_2$ where $T_1$ is tension between $+q$ and $+2q$?

Two parallel infinite line charges with linear charge densities $+\lambda$ and $-\lambda$ are placed a distance $2R$ apart. What is the force per unit length on a third line charge $+\lambda$ placed exactly midway between them?

Three charges $+q, +q, +q$ are at the corners of an equilateral triangle. What is the force on any one charge?

A semi-circular arc of radius $R$ is charged with a total charge $Q$. What is the force on a charge $q$ placed at the center of curvature?

Electric dipole moment is a:

Which component of the electric field vanishes on the equatorial line of a dipole?

The angle between the axial line and the equatorial line of a dipole is:

If the electric field is $10 \, N/C$ and dipole moment is $2 \, C \cdot m$, the maximum torque is:

An electric dipole of moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$. If $U$ represents the electrostatic potential energy of the dipole and $\tau$ represents the magnitude of the torque acting on it, at what angle $\theta$ between $\vec{p}$ and $\vec{E}$ is the magnitude $|U|$ equal to $\tau$?

Three point charges $-q$, $+2q$, and $-q$ are arranged in the $xy$-plane. The charge $+2q$ is situated at the origin $(0,0)$, one $-q$ charge is at $(a,0)$, and the other $-q$ charge is at $(0,a)$. What is the magnitude of the net electric dipole moment of this system?

A small electric dipole is placed at a distance $r$ from a fixed positive point charge $+Q$. The dipole is oriented such that its dipole moment vector $\vec{p}$ points radially away from the point charge. What is the nature of the net electrostatic force experienced by the dipole?

Two small dipoles $p \hat{i}$ and $p \hat{i}$ are placed at $(0, 0, 0)$ and $(a, 0, 0)$ respectively. The force between them is:

A short dipole of moment $p$ is kept at a distance $r$ from an infinite line charge of linear density $\lambda$. The dipole is oriented radially away from the line. The force on the dipole is:

An electric dipole of moment $p$ is placed at an angle $\theta$ with a uniform electric field $E$. The magnitude of torque is $\tau$. The potential energy $U$ is related to $\tau$ as:

An electric dipole in a uniform electric field will always experience a torque unless $\theta$ is:

Two charges $+1\mu C$ and $-1\mu C$ are separated by $2 cm$. What is the dipole moment?

The dimensions of dipole moment are:

The SI unit of electric dipole moment is:

An electric dipole of dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$. The work done in rotating the dipole from its stable equilibrium position ($\theta = 0^{\circ}$) to the position where it is perpendicular to the electric field ($\theta = 90^{\circ}$) is $W$. What is the magnitude of the torque experienced by the dipole when it is oriented at an angle of $30^{\circ}$ with the direction of the electric field?

The frequency of oscillation of a dipole (moment of inertia $I$) when slightly displaced from stable equilibrium is:

A dipole of moment $p$ is placed in a field $E$. If the dipole is rotated from $\theta = 90^{\circ}$ to $\theta = 0^{\circ}$, the work done by the field is:

A dipole is placed in a field. If the potential energy $U$ is plotted against the angle $\theta$, the minimum value occurs at:

In a uniform electric field, a dipole experiences a maximum torque when the angle between $\vec{p}$ and $\vec{E}$ is:

A dipole with $p = 10^{-5}$ Cm is placed in $E = 10^{3}$ N/C. The work done to rotate it from $0^\circ$ to $180^\circ$ is:

Surface charge density is used for objects like:

Linear charge density is used for objects like:

If the radius of a charged spherical shell is doubled while the total charge remains constant, the electric field at a point far outside (distance $r$):

The principle of superposition allows us to find the total electric field by:

Which of the following distributions will have an electric field that does not decrease with distance?

The field $E$ at a point $P$ due to a continuous charge distribution is found by:

A long straight wire has a charge of $1 \, \mu C$ per meter. The electric field at a distance of $1 \, m$ is (approx):

A plastic rod is bent into a circle of radius $R$. One quarter has charge $+Q$ and the rest has $-3Q$ uniformly. The field at the center is the same as that of a point charge:

A thin rod of length $L$ has charge $Q$ distributed uniformly. The field at a point $P$ at distance $L$ from one end on its axis is:

An infinite cylinder has $\rho$ uniform. The field $E$ at distance $r > R$ varies as: