iCON Education - Electrostatics Objective Physics Vol-2 Test

When $10^{14}$ electrons are removed from a neutral metal sphere, the charge on the sphere becomes

Concept: Quantization of charge, where the total charge on a body is given by $q = ne$, and a positive charge indicates a deficiency or shortage of electrons.

A conductor has $14.4 \times 10^{-19}\ \text{C}$ positive charge. The conductor has (charge on electron $= 1.6 \times 10^{-19}\ \text{C}$)

9 electrons in excess

27 electrons in short

27 electrons in excess

9 electrons in short

Concept: An $\alpha$-particle is a helium nucleus ($He^{2+}$) which contains two protons and two neutrons. Since neutrons are neutral, the total charge of the $\alpha$-particle is equal to the charge of two protons, which is twice the elementary charge $e$.

Charge on $\alpha$-particle is

$4.8 \times 10^{-19}\text{ C}$

$1.6 \times 10^{-19}\text{ C}$

$3.2 \times 10^{-19}\text{ C}$

$6.4 \times 10^{-19}\text{ C}$

Concept: Charging by rubbing creates static electricity through the transfer of electrons between two objects. The material that donates electrons becomes positively charged, while the material that receives electrons becomes negatively charged.

When a glass rod is rubbed with silk, it

gains electrons from silk

gives electrons to silk

gains protons from silk

gives protons to silk

Concept: Charging and electrostatic induction involve the movement of free electrons. When a body is connected to the earth, electrons move between the earth and the body to neutralize or redistribute potential, depending on the net charge or surrounding electric field present near the body.

When a body is earth connected, electrons from the earth flow into the body. This means the body is

Concept: According to Coulomb's law, the electrostatic force between two point charges forms an action-reaction pair. This means the force exerted by the first charge on the second charge is equal in magnitude and opposite in direction to the force exerted by the second charge on the first charge, regardless of the individual magnitudes of the charges.

There are two charges $+1 \mu\text{C}$ and $+5 \mu\text{C}$. The ratio of the forces acting on them will be

Concept: The gravitational force between two masses is given by Newton's law of gravitation, and the electrostatic force between two charges is given by Coulomb's law. Comparing their orders of magnitude for subatomic particles like electrons reveals the relative dominance of electrostatic interactions over gravitational interactions at small scales.

$F_g$ and $F_e$ represents gravitational and electrostatic force respectively between electrons situated at a distance $10\text{ cm}$. The ratio of $F_g / F_e$ is of the order of

Concept: The superposition principle states that the net electrostatic force acting on a given charge is the vector sum of the forces exerted on it by all other individual charges. The force between any two point charges is determined by Coulomb's law.

Two similar small spheres having $+q$ and $-q$ charge are kept at a certain distance. $F$ force acts between them. If in the middle of two spheres, another similar sphere having $+q$ charge is kept, then it will experience a force in magnitude and direction as

zero having no direction

$8F$ towards $+q$ charge

$8F$ towards $-q$ charge

$4F$ towards $+q$ charge

Concept: Coulomb's law states that the electrostatic force between two point charges is inversely proportional to the square of the distance between them, given by $F \propto \frac{1}{r^2}$. When the separation distance changes, the new force can be found using the inverse square relationship.

The force between two charges $0.06\text{ m}$ apart is $5\text{ N}$. If each charge is moved towards the other by $0.01\text{ m}$, then the force between them will become

Concept: When charges are immersed in a dielectric medium instead of vacuum or air, the electrostatic force between them decreases by a factor equal to the dielectric constant $K$ of the medium.

Two charged spheres separated at a distance $d$ exert a force $F$ on each other. If they are immersed in a liquid of dielectric constant $2$, then what is the force? (if all conditions are same)

Concept: The net electrostatic force on a point charge due to multiple surrounding charges is obtained by finding the vector sum of individual forces exerted by each charge, as determined by Coulomb's law and the principle of superposition.

Electric charges of $1\mu\text{C}$, $-1\mu\text{C}$ and $2\mu\text{C}$ are placed in air at the corners $A$, $B$ and $C$ respectively of an equilateral triangle $ABC$ having length of each side $10\text{ cm}$. The resultant force on the charge at $C$ is

Concept: When two identical conducting spheres are brought into physical contact, total charge redistributes equally between them due to their identical capacitance. The electrostatic force before and after contact can then be calculated using Coulomb's law.

Two small conducting spheres of equal radius have charges $+10\mu\text{C}$ and $-20\mu\text{C}$ respectively and placed at a distance $r$ from each other. They experience force $F_1$. If they are brought in contact and separated to the same distance, they experience force $F_2$. The ratio of $F_1$ to $F_2$ is

Concept: The net electrostatic force on a point charge in a system of multiple charges is determined by using Coulomb's law for each interacting pair and combining them via the principle of superposition by vector addition.

Equal charges $Q$ are placed at the four corners $A$, $B$, $C$ and $D$ of a square of length $a$. The magnitude of the force on the charge at $B$ will be

$\frac{3Q^2}{4 \pi \varepsilon_0 a^2}$

$\frac{Q^2}{4 \pi \varepsilon_0 a^2}$

$\left(1 + \frac{2\sqrt{2}}{2}\right)\frac{Q^2}{4 \pi \varepsilon_0 a^2}$

$\left(2 + \frac{1}{\sqrt{2}}\right)\frac{Q^2}{4 \pi \varepsilon_0 a^2}$

Concept: Charge conservation and equal sharing of charge upon physical contact between identical conducting spheres, combined with Coulomb's law and the superposition principle, govern the final force on the relocated sphere.

Two equally charged, identical metal spheres $A$ and $B$ repel each other with a force $F$. The spheres are kept fixed with a distance $r$ between them. A third identical, but uncharged sphere $C$ is brought in contact with $A$ and then placed at the mid-point of the line joining $A$ and $B$. The magnitude of the net electric force on $C$ is

Concept: A third charge is in mechanical equilibrium under the electrostatic forces exerted by two surrounding like charges if the net force acting on it is zero, meaning the forces from the two charges must be equal in magnitude and opposite in direction.

Two charges $+4e$ and $+e$ are at a distance $x$ apart. At what distance, a charge $q$ must be placed from charge $+e$, so that it is in equilibrium?

Concept: The principle of superposition states that the net electrostatic force on any given charge is the vector sum of all individual forces exerted on it by the other charges in the system. For the net force to be zero, the vector sum of these forces must vanish.

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

Concept: A system of charges is in complete mechanical equilibrium when every individual charge in the system experiences a net electrostatic force of zero.

A charge $q$ is lying at mid-point of the line joining the two similar charges $Q$. The system will be in equilibrium if the value of $q$ is

Concept: Coulomb's law dictates that the electrostatic force between two point charges depends directly on the product of their individual net charges and inversely on the square of the distance between them. Adding or removing charge alters the individual magnitudes while keeping the separation distance constant.

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

$4\text{ N}$ (repulsive)

$4\text{ N}$ (attractive)

$12\text{ N}$ (attractive)

$8\text{ N}$ (repulsive)

Concept: According to Coulomb's law, the electrostatic force between two point charges depends only on the magnitudes of the two charges and the distance between them, and it is independent of the presence of any other surrounding charges.

A charge $q_1$ exerts some force on a second charge $q_2$. If a third charge $q_3$ is brought near $q_2$, the force exerted by $q_1$ on $q_2$

increases if $q_3$ is of same sign as $q_1$ and decreases if $q_3$ is of opposite sign as $q_1$

Concept: Coulomb's law states that the electrostatic force between two point charges is inversely proportional to the square of the distance between them, while being directly proportional to the product of their charges.

Three equal charges are placed on the three corners of a square. 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 $(F_{12} / F_{13})$ is

Concept: When two identical conducting spheres with charges of opposite signs are connected by a conducting wire, charges redistribute such that the total charge is conserved and shared equally between them, resulting in identical positive or negative charges on both spheres.

The centres of two identical small conducting spheres are $1\text{ m}$ apart. They carry charges of opposite kind and attract each other with a force $F$. When they are connected by a conducting thin wire they repel each other with a force $F/3$. What is the ratio of magnitude of charges carried by the spheres initially?

Concept: Electrostatic induction causes redistribution of charges on an uncharged conducting sphere placed in an external electric field, creating an induced negative charge closer to the positive plate and an induced positive charge further away, leading to a net attractive force due to closer proximity of opposite charges.

A metallic sphere having no net charge is placed near a finite metal plate carrying a positive charge. The electric force on the sphere will be

parallel to the plate

Concept: Electric field lines represent the strength and direction of an electric field. The density or crowding of electric field lines indicates the magnitude of the electric field, where closely spaced lines denote a stronger electric field and widely spaced lines denote a weaker electric field.

Figure shows the electric lines of force emerging from a charged body. If the electric field at $A$ and $B$ are $E_A$ and $E_B$ respectively and if the distance between $A$ and $B$ is $r$, then

$E_A = \frac{E_B}{r}$

$E_A = \frac{E_B}{r^2}$

Concept: Superposition principle of electric field vectors due to point charges and symmetry.

$ABC$ is an equilateral triangle. Charges $+q$ are placed at each corner. The electric intensity at $O$ will be

$\frac{1}{4\pi\varepsilon_0} \frac{q}{r^2}$

$\frac{1}{4\pi\varepsilon_0} \frac{q}{r}$

$\frac{1}{4\pi\varepsilon_0} \frac{3q}{r^2}$

Concept: Electric field on the surface of a charged conducting sphere and dielectric breakdown of air.

The insulation property of air breaks down at $E = 3 \times 10^6$ V/m. The maximum charge that can be given to a sphere of diameter $5$ m is approximately (in coulombs)

Concept: Null point position where the electric field due to two like point charges becomes zero.

The distance between the two charges $25$ microcoulombs and $36$ microcoulombs is $11$ cm. At what point on the line joining the two, the intensity will be zero?

At a distance of $5$ cm from $25$ microcoulombs

At a distance of $5$ cm from $36$ microcoulombs

At a distance of $4$ cm from $25$ microcoulombs

At a distance of $4$ cm from $36$ microcoulombs

Concept: Electric field intensity near the surface of a charged conductor using Gauss's law.

The electric field near a conducting surface having a uniform surface charge density $\sigma$ is given by

$\frac{\sigma}{\varepsilon_0}$ and is parallel to the surface

$\frac{2\sigma}{\varepsilon_0}$ and is parallel to the surface

$\frac{\sigma}{\varepsilon_0}$ and is normal to the surface

$\frac{\sigma}{2\varepsilon_0}$ and is normal to the surface

Concept: Dimensional analysis and relation between units of electric field, force, potential, and distance.

The unit of electric field is not equivalent to

Concept: Behavior of electric field lines near the surface and inside a conductor in electrostatic equilibrium.

A metallic solid sphere is placed in a uniform electric field. The lines of force follow the path(s) shown in figure as

Concept: Density of electric field lines as a measure of electric field strength.

The figure shows some of the electric field lines corresponding to an electric field. The figure suggests

Concept: Equipotential surfaces, charge distribution on connected conductors, and electric field at the surface of a spherical conductor.

Two spheres of radius $a$ and $b$ respectively are charged and joined by a wire. The ratio of electric field of the spheres is

Concept: Symmetry of charge distribution and vector superposition of electric fields at the center of a symmetric body.

A cube of side $b$ has a charge $q$ at each of its vertices. The electric field due to this charge distribution at the centre of this cube will be $\frac{1}{4\pi\varepsilon_0}$ times

Concept: Superposition principle of electric field vectors and symmetry of charge distributions in regular polygons.

Figures below show regular hexagons, with charges at the vertices. In which of the following cases the electric field at the centre is not zero?