Electric Charge & Coulomb's Law

Two spherical hollow spheres of radii '$R_1$' and '$R_2$' are charged with same charge. Let '$\sigma_1$' and '$\sigma_2$ ' are their respective charge densities, then the ratio $\sigma_1$ to $\sigma_2$ is

Two point charges placed at a certain distance $r$ in air exert force $F$ on each other. Then the distance $r_1$ at which these charges will exert the same force in a medium of dielectric constant $K$ is

Two point charges $q_1$ and $q_2$ are '$l$' distance apart. If one of the charges is doubled and the distance between them is halved. The magnitude of the force becomes 'n' times, where 'n' is

Two equal point charges exert a force F on each other when they are placed distance 'd' apart in air. When they are placed distance 'D' apart in a medium of dielectric constant K, they exert the same force. The distance D is equal to

If two charges $q_1$ and $q_2$ are separated with distance 'd' and placed in a medium of dielectric constant $K$. What will be the equivalent distance between charges in air for the same electrostatic force?

Two point charges $q_1 = 3\ \mu\text{C}$ and $q_2 = -4\ \mu\text{C}$ are placed at points $(2\hat{i} + 3\hat{j} + 3\hat{k})$ and $(\hat{i} + \hat{j} + \hat{k})$ respectively. Force on charge $q_2$ is ______ N. (Take $\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}$ SI Units)

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

Two point charges +e and +4e are kept at a distance 'd' units apart. Third point charge +q is placed between the two charges at a distance 'x' units from charge +e so as to be in equilibrium. The value of 'x' is

A point charge 'Q' is placed at the centre of the line joining two equal charges '+q' and '+q'. The value of 'Q' when the system is in equilibrium is

Two charged identical metal spheres A and B repel each other with a force $3 \times 10^{-5}$ N. Another identical uncharged sphere C is touched with A and then placed at the mid-point between A and B. Net force on C is $x \times 10^{-5}$ N. The value of $x$ is

Charge $q_2$ of mass '$m$' revolves around a stationary charge $q_1$ in a circular orbit of radius '$r$'. The orbital periodic time of $q_2$ would be $\left(k = \frac{1}{4\pi\epsilon_0}\right)$

Two point charges, $+2C$ and $+6C$ repel each other with a force of $12$N. If a charge of $(-4C)$ is given to each of these charges, the force now is

Two point charges placed in air separated by distance $R$ exert a force $F$ on each other. Now the space between those charges is filled with dielectric constant $K$. At distance $R_1$ between the charges, the same force is exerted as $F$. Then

Three charges $q,\ Q$ and $+4q$ are placed in a straight line of length $d$ at points at distance $0,\ \frac{d}{3},\ \frac{2d}{3}$ respectively. In order to make the net force on $q$ be zero, the value of $Q$ should be

Two charged particles each having a charge '$+q$' and mass 'm' are kept at a distance 'd'. If they are in equilibrium under the gravitational force and the electric force between them, then the ratio $\frac{q}{m}$ (specific charge) of each particle is ($G$- Universal gravitation constant, $\varepsilon_0$ = permittivity of free space)

Two particles of charges $q_1 = 8q$ and $q_2 = -2q$ are placed as shown in figure. At what point away from $q_2$ on x-axis can a proton be placed placed so that it is in equilibrium?

Two point charges $q_1$ and $q_2$ are ' $l$ ' distance apart. If one of the charges is doubled and distance between them is halved. The magnitude of force becomes $n$ times, where $n$ is

A positive ion $A$ and a negative ion $B$ has charges $6.67 \times 10^{-19}\text{ C}$ and $9.6 \times 10^{-10}\text{ C}$, and masses $19.2 \times 10^{-27}\text{ kg}$ and $9 \times 10^{-27}\text{ kg}$ respectively. At an instant, the ions are separated by a certain distance $r$. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is $P \times 10^{-13}$, where the value of P is _________.

(Take $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}\text{ N m}^2\text{ C}^{-2}$ and universal gravitational constant as $6.67 \times 10^{-11}\text{ N m}^2\text{ kg}^{-2}$)

Three equal charges are placed on the three corners of a square as shown below. If the magnitude of force between ' $q_1$ ' and ' $q_2$ ' is ' $F_{12}$ ' and that between ' $q_1$ ' and ' $q_3$ ' is $F_{13}$, then the ratio of $F_{13}$ to $F_{12}$ is

Two equally charged small balls placed at a fixed distance experience a force ' $F$ '. A similar uncharged ball after touching one of them is placed at the middle point between the two balls. the force experienced by this ball is

Two identical charged conducting spheres $A$ and $B$ have their centres separated by a certain distance. Charge on each sphere is $q$ and the force of repulsion between them is $F$. A third identical uncharged conducting sphere is brought in contact with sphere $A$ first and then with $B$ and finally removed from both. New force of repulsion between spheres $A$ and $B$ (Radii of $A$ and $B$ are negligible compared to the distance of separation so that for calculating force between them they can be considered as point charges) is best given as:

A small uncharged conducting sphere is placed in contact with an identical sphere but having $4 \times 10^{-8}\text{ C}$ charge and then removed to a distance such that the force of repulsion between them is $9 \times 10^{-3}\text{ N}$. The distance between them is (Take $\frac{1}{4\pi\epsilon_0}$ as $9 \times 10^{9}$ in SI units)

Three charges ' $+3q$ ', ' $Q$ ' and ' $+q$ ' are placed in a straight line of length ' $l$ ' at points at distances $0,\ \frac{l}{2}$ and $l$ respectively. The value of Q in order to have the net force on +q to be zero, $Q = xq$. The value of $x$ is

Two charges $q_1 = +6q$ and $q_2 = -3q$ placed as shown in figure. A proton is placed on x -axis away from $q_2$. To remain proton in equilibrium, the distance between $q_1$ and proton is

A metal cube of side $5\text{ cm}$ is charged with $6\ \mu\text{C}$. The surface charge density on the cube is

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of:

Two equal point charges ' $q$ ' each exert a force ' $F$ ' on each other, when they are placed distance ' $x$ ' apart in air. When the same charges are placed distance ' $y$ ' apart in a medium of dielectric constant ' $k$ ', they exert the same force. The ratio of distance ' $y$ ' to ' $x$ ' is equal to

Force between two point charges $q_1$ and $q_2$ placed in vacuum at '$r$' cm apart is $F$. Force between them when placed in a medium having dielectric constant $K = 5$ at '$r/5$' $\text{cm}$ apart will be:

Two point charges $+q_1$ and $q_2$ repel each other with a force of $100\text{ N}.\ q_1$ is increased by $10\%$ and $q_2$ is decreased by $10\%$. If they are kept at their original positions the change in the force of repulsion between them is

Two point charges $(A$ and $B) + 4q$ and $-4q$ are placed along a line separated by a distance I '. Force acting between them is F. If $25\%$ of charge from point $A$ is transferred to that at point B, the force between the charges now becomes

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

A charge $+Q$ is placed at each of the diagonally opposite corners of a square. A charge -q is placed at each of the other diagonally opposite corners as shown. If the net electrical force on $+Q$ is zero, then $\frac{+Q}{-q}$ is equal to

Charges $3Q, q$ and Q are placed along x -axis at positions $x = 0, x = \frac{1}{3}$ and $x = 1$ respectively. When the force on charge Q is zero, the value of $q$ is

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $\theta$ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is $1.5\text{ g/cc}$, the dielectric constant of water will be __________. (Take density of water $= 1\text{ g/cc}$)

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

A thin metallic wire having cross sectional area of $10^{-4}\text{ m}^{2}$ is used to make a ring of radius $30\text{ cm}$. A positive charge of $2\pi\text{ C}$ is uniformly distributed over the ring, while another positive charge of 30 $\text{pC}$ is kept at the centre of the ring. The tension in the ring is ______ $\text{N}$; provided that the ring does not get deformed (neglect the influence of gravity). (given, $\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}$ SI units)

Select the correct statement from the following.

Two positively charged identical spheres separated by a distance 'd' exert some force (F) on each other when they are kept in air. If both the spheres are immersed in a liquid of dielectric constant 5, the force experienced by each is (All other parameters are unchanged.)

A $10\ \mu\text{C}$ charge is divided into two parts and placed at $1\text{ cm}$ distance so that the repulsive force between them is maximum. The charges of the two parts are:

If two charges q${}_1$ and q${}_2$ are separated with distance 'd' and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?

Three point charges $q, -2q$ and $2q$ are placed on $x$-axis at a distance $x = 0, x = \frac{3}{4}R$ and $x = R$ respectively from origin as shown. If $q = 2 \times 10^{-6}\text{ C}$ and $R = 2\text{ cm}$, the magnitude of net force experienced by the charge $-2q$ is ___________ N.

As shown in the figure, a configuration of two equal point charges $(q_0 = +2\,\mu\text{C})$ is placed on an inclined plane. Mass of each point charge is $20\text{ g}$. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height $h = x \times 10^{-3}\text{ m}$.

The value of $x$ is ____________.

(Take $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}\text{ N m}^{2}\text{C}^{-2}, g = 10\text{ m s}^{-2}$)

A point charge $q_1 = 4q_0$ is placed at origin. Another point charge $q_2 = -q_0$ is placed at $x = 12$ cm. Charge of proton is $q_0$. The proton is placed on $x$ axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the origin is ___________ cm.

A charge of $4\ \mu\text{C}$ is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be:

Three equal charges '$q_1$', '$q_2$ ' and '$q_3$' are placed on the three corners of a square of side 'a'. If the force between $q_1$ and $q_2$ is '$F_{12}$' and that between $q_1$ and $q_3$ is '$F_{13}$', then the ratio of magnitudes $\left(\frac{F_{12}}{F_{13}}\right)$ is

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:

Three point charges of magnitude $5\,\mu\text{C}, 0.16\,\mu\text{C}$ and $0.3\,\mu\text{C}$ are located at the vertices $A, B, C$ of a right angled triangle whose sides are $AB = 3\text{ cm}, BC = 3\sqrt{2}\text{ cm}$ and $CA = 3\text{ cm}$ and point $A$ is the right angle corner. Charge at point $A$ experiences ____________ $\text{N}$ of electrostatic force due to the other two charges.

Two identical charged particles each having a mass 10 g and charge 2.0 $\times$ 10$-$7C are placed on a horizontal table with a separation of L between them such that they stay in limiting equilibrium. If the coefficient of friction between each particle and the table is 0.25, find the value of L. [Use g = 10 ms${}^{-2}$]

Three identical charged balls each of charge 2 C are suspended from a common point P by silk threads of 2 m each (as shown in figure). They form an equilateral triangle of side 1m. The ratio of net force on a charged ball to the force between any two charged balls will be:

Two positive ions, each carrying a charge 'q' are separated by a distance 'd'. If 'F' is the force of repulsion between the ions, the number of electrons from each ion will be ($e$ = charge on $\text{electron}, \varepsilon_0$ = permittivity of free space)

When a piece of polythene is rubbed with wool, a negative charge of $4 \times 10^{-7}\text{ C}$ is developed on the polythene. The number of electrons transferred from wool to polythene is $[e = 1.6 \times 10^{-19}\text{ C}]$

'$F$' is the force between the two identical charged particles placed at a distance '$Y$' from each other. If the distance between the charges is reduced to half the previous distance then force between them becomes

A certain charge Q is divided into two parts q and (Q $-$ q). How should the charges Q and q be divided so that q and (Q $-$ q) placed at a certain distance apart experience maximum electrostatic repulsion?

Three charges each of $+1\ \mu\text{C}$ are placed at the corners of an equilateral triangle. If the repulsive force between any two charges is $F$, then the net force on either charge will be [$\cos 60^\circ = 0.5$]

A point charge $Q$ is placed at the centre of the line joining two equal point charges $+q$ and $+q$. The value of $Q$ if the system of the charges is in equilibrium, is

Two particles A and B having charges 20$\mu$C and $-5\mu$C respectively are held fixed with a separation of 5 cm. At what position a third charged particle should be placed so that it does not experience a net electric force?

Two point charges $+3\ \mu\text{C}$ and $+8\ \mu\text{C}$ repel each other with a force of $40\text{ N}$. If a charge of $-5\ \mu\text{C}$ is added to each of them, then force between them will become

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 __________ $\times$ 10$-$9 N.

[Given: $4\pi\varepsilon_0 = \frac{1}{9 \times 10^{9}}$ SI unit]

An infinite number of point charges, each carrying 1 $\mu$C charge, are placed along the y-axis at y = 1 m, 2 m, 4 m, 8 m ...............

The total force on a 1C point charge, placed at the origin, is x $\times$ 103 N.

The value of x, to the nearest integer, is __________. [Take $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}$ Nm2/C2]

Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'l'. What is the equilibrium separation when each thread makes a small angle '$\theta$' with the vertical?

Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.20 m. The charge on each of the sphere is $\frac{a}{21} \times 10^{-8}$ C. The value of 'a' will be ___________. [Given g = 10 ms${}^{-2}$]

The acceleration of an electron due to the mutual attraction between the electron and a proton when they are 1.6 Å apart is,

$(m_e \simeq 9 \times 10^{-31}\text{ kg},\ e = 1.6 \times 10^{-19}\text{ C})$

(Take $\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}\text{ N m}^2\text{ C}^{-2}$)

In case of dimensions of electric field and electric dipole moment the power of mass is respectively,

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:

Two point charges A and B, having charges +Q and – Q respectively, are placed at certain distance apart and force acting between them is F. If 25% charge of A is transferred to B, then force between the charges becomes:

Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameters, and the force between them is F. A third identical conducting sphere, C, is uncharged. Sphere C is first touched to A, then to B, and then removed. As a result, the force between A and B would be equal to:

Suppose the charge of a proton and an electron differ slightly. One of them is $-$e, the other is (e + $\Delta$e). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (musch greater than atomic size) apart is zero, then $\Delta$e is of the order of [Given: mass of hydrogen mh = 1.67 $\times$ 10$-$27 kg]

Two identical charged spheres suspended from a common point by two massless strings of lengths $l$, are initially at a distance d(d < < $l$) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as

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

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

Two small equal point charges of magnitude $q$ are suspended from a common point on the ceiling by insulating mass less strings of equal lengths. They come to equilibrium with each string making angle $\theta$ from the vertical. If the mass of each charge is $m$, then the electrostatic potential at the centre of line joining them will be $\left(\frac{1}{4\pi\epsilon_0} = k\right)$.

Two balls of same mass and carrying equal charge are hung from a fixed support by threads of length $l$. At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, x between the balls is proportional to:

Two identical charged spheres suspended from a common point by two massless strings of length $l$ are initially a distance $d\,(d << l)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result charges approach each other with a velocity $v$. Then as a function of distance $x$ between them,

Two positive ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron)

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^\circ$ with each other. When suspended in a liquid of density $0.8\text{ g cm}^{-3},$ the angle remains the same. If density of the material of the sphere is $1.6\text{ g cm}^{-3},$ the dielectric constant of the liquid is

A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero, then $Q/q$ equals:

Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges on them repel each other with a force $F$ when kept apart at some distance. A third spherical conductor having same radius as that of $B$ but uncharged is brought in contact with $B,$ then brought in contact with $C$ and finally removed away from both. The new force of repulsion between $B$ and $C$ is

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