Vardaan Learning Institute

The specific charge ($e/m$ ratio) of an electron is approximately ____________ $\text{C/kg}$.

In a neutral, isolated atom, the number of protons is strictly ____________ to the number of electrons.

A body has a charge of $-80 \mu\text{C}$. The number of excess electrons on it is:
(A) $5 \times 10^{13}$     (B) $5 \times 10^{14}$     (C) $1.6 \times 10^{14}$     (D) $8 \times 10^{13}$

Which of the following charges cannot exist in nature?
(A) $3.2 \times 10^{-19} \text{ C}$     (B) $4.8 \times 10^{-19} \text{ C}$     (C) $6.4 \times 10^{-19} \text{ C}$     (D) $5.4 \times 10^{-19} \text{ C}$

Calculate the total charge on an alpha ($\alpha$) particle.

How many electrons must be removed from a neutral piece of metal to give it a positive charge of $1.0 \times 10^{-7} \text{ C}$?

Does the mass of a body strictly change when it is given a negative charge? Explain briefly.

Is it possible for two similarly charged bodies to attract each other? Give a reason.

What is the macroscopic physical cause behind the quantization of electric charge?

Match the basic properties of charge with their defining mathematical or physical expressions:

(a) Quantization of charge	(i) $Q_{total} = q_1 + q_2 + ... + q_n$
(b) Additivity of charge	(ii) $\Delta Q_{isolated\_system} = 0$
(c) Conservation of charge	(iii) $q = \pm ne$

The value of the dielectric constant ($K$ or $\epsilon_r$) for pure water is approximately ____________.

If the distance between two point charges is halved, the electrostatic force between them becomes ____________ times the original force.

The force between two charges in vacuum is $F$. If a thick brass plate is introduced completely between them, the force becomes:
(A) $F$     (B) $F/2$     (C) Infinity     (D) Zero

The ratio of electric force ($F_e$) to gravitational force ($F_g$) between an electron and a proton separated by a distance is of the order of:
(A) $10^{39}$     (B) $10^{36}$     (C) $10^{42}$     (D) $10^{-39}$

Two point charges of $+5 \mu\text{C}$ and $+10 \mu\text{C}$ are placed $20 \text{ cm}$ apart in a vacuum. Calculate the electrostatic force between them.

The electrostatic force on a small sphere of charge $0.4 \mu\text{C}$ due to another small sphere of charge $-0.8 \mu\text{C}$ in air is $0.2 \text{ N}$. What is the distance between the two spheres?

In the previous question (Q16), what is the magnitude of the force exerted on the second sphere by the first sphere?

Define $1 \text{ Coulomb}$ of charge strictly using Coulomb's law.

State two major limitations of Coulomb's law in electrostatics.

Match the medium to its corresponding approximate dielectric constant ($K$):

(a) Vacuum / Air	(i) $80$
(b) Water	(ii) Infinity ($\infty$)
(c) Conducting Metals	(iii) $1$ (approx)

The electric field inside a solid conducting sphere given a charge $Q$ is mathematically ____________.

A uniformly spaced, parallel set of electric field lines represents a ____________ electric field.

The dimensional formula of Electric Field Intensity is:
(A) $[M L T^{-2} A^{-1}]$     (B) $[M L T^{-3} A^{-1}]$     (C) $[M L^2 T^{-3} A^{-2}]$     (D) $[M L T^{-3} A]$

A proton and an electron are placed in the exact same uniform electric field. They will experience:
(A) Equal forces in magnitude and direction.     (B) Equal forces in magnitude but opposite in direction.
(C) Equal accelerations.     (D) Accelerations of the same magnitude but opposite direction.

Calculate the magnitude of the electric field at a distance of $5 \text{ cm}$ from a point charge of $10 \mu\text{C}$.

Determine the electric field strength required to just balance the weight of an electron. (Given: $m_e = 9.1 \times 10^{-31} \text{ kg}$, $e = 1.6 \times 10^{-19} \text{ C}$, $g = 9.8 \text{ m/s}^2$).

Calculate the force experienced by an alpha particle placed in an electric field of $3 \times 10^4 \text{ N/C}$.

Why do electric field lines never form closed continuous loops?

Can a charged particle always move along the path of an electric field line? Explain.

Match the charge configuration with its corresponding electric field line pattern:

(a) Isolated positive point charge	(i) Radial, pointing inwards
(b) Isolated negative point charge	(ii) Parallel, equally spaced straight lines
(c) Two oppositely charged large parallel plates	(iii) Radial, pointing outwards

The net translational force acting on an electric dipole placed in a *uniform* electric field is always ____________.

Electric flux is a ____________ physical quantity (scalar/vector).

A practical non-SI unit often used for electric dipole moment is the:
(A) Faraday     (B) Debye     (C) Gauss     (D) Maxwell

If an electric dipole is placed in a non-uniform electric field, it generally experiences:
(A) Only a force     (B) Only a torque     (C) Both a net force and a torque     (D) Neither force nor torque

Two point charges of $\pm 10 \mu\text{C}$ are placed $5 \text{ mm}$ apart. Calculate the magnitude of the electric dipole moment.

Using the dipole from Q35, calculate the electric field at a point on its axial line at a distance of $15 \text{ cm}$ from its center.

A circular plane sheet of radius $10 \text{ cm}$ is placed in a uniform electric field of $5 \times 10^5 \text{ N/C}$, making an angle of $60^\circ$ with the field lines. Calculate the electric flux through the sheet.

Define an "ideal" or "point" electric dipole.

What is the work done in rotating a dipole from its position of stable equilibrium to unstable equilibrium in a uniform electric field?

Match the angle $\theta$ (between $\vec{p}$ and $\vec{E}$) to the resulting torque magnitude ($\tau$):

(a) $\theta = 0^\circ$	(i) Maximum torque ($pE$)
(b) $\theta = 90^\circ$	(ii) Zero torque (Unstable equilibrium)
(c) $\theta = 180^\circ$	(iii) Zero torque (Stable equilibrium)

The physical SI unit of surface charge density ($\sigma$) is ____________.

A Gaussian surface must ideally be chosen such that the electric field is either ____________ or ____________ to the surface at every point.

If a charge $q$ is placed exactly at the center of one face of a cube, the total flux passing through the cube is:
(A) $q/\epsilon_0$     (B) $q/2\epsilon_0$     (C) $q/6\epsilon_0$     (D) $q/8\epsilon_0$

Gauss's law in electrostatics is fundamentally a consequence of:
(A) Conservation of charge     (B) Quantization of charge     (C) The inverse square dependence on distance     (D) Superposition principle

A spherical Gaussian surface encloses a net charge of $8.854 \times 10^{-8} \text{ C}$. Calculate the total electric flux passing through the surface.

If the radius of the Gaussian surface in the previous question (Q45) is doubled, how would the electric flux change?

A point charge $+10 \mu\text{C}$ is at a distance $5 \text{ cm}$ directly above the center of a square of side $10 \text{ cm}$. What is the magnitude of the electric flux through the square?

Is Gauss's law valid for a non-uniform electric field?

What is the net electric flux through a closed surface if it completely encloses three identical electric dipoles?

Match the type of charge distribution to its appropriate standard symbol:

(a) Linear Charge Distribution	(i) $\rho$
(b) Surface Charge Distribution	(ii) $\lambda$
(c) Volume Charge Distribution	(iii) $\sigma$

The electric field just outside a charged macroscopic conducting plate is given by the formula ____________.

The electric field at the surface of a charged spherical shell of radius $R$ and total charge $Q$ is ____________.

Electric field intensity due to a long straight uniformly charged wire varies with distance $r$ as:
(A) $r$     (B) $1/r$     (C) $1/r^2$     (D) $1/r^3$

Two large, thin metal plates are parallel and close to each other. On their inner faces, they have surface charge densities of opposite signs but equal magnitude $\sigma$. The electric field between the plates is:
(A) Zero     (B) $\sigma/2\epsilon_0$     (C) $\sigma/\epsilon_0$     (D) $2\sigma/\epsilon_0$

An infinite line charge produces a field of $9 \times 10^4 \text{ N/C}$ at a distance of $2 \text{ cm}$. Calculate the linear charge density.

Referring to Q54, what is the electric field in the outer regions (above the top plate and below the bottom plate)?

Why is the electric field strictly zero everywhere inside a hollow charged conductor under electrostatic conditions?

Sketch a generic graph showing the variation of electric field $E$ with distance $r$ from the center of a uniformly charged thin spherical shell of radius $R$.

Can we strictly use Gauss's law to analytically find the exact electric field of a *finite* line charge at any arbitrary point? Briefly explain.

Match the geometrical charge source to how its electric field $E$ depends on distance $r$ (for outside points):

(a) Point Charge / Spherical Shell	(i) $E \propto 1/r^3$
(b) Infinite Line Charge	(ii) $E \propto 1/r^2$
(c) Short Electric Dipole (Axial/Equatorial)	(iii) $E \propto 1/r$