Practice Questions

Recall the SI unit and the approximate value of the permittivity of free space, $\varepsilon_0$.

Compare the behavior of excess electric charge when placed on an isolated metallic sphere versus an isolated plastic sphere.

Analyze how the force between two point charges, $q_1$ and $q_2$, is affected by the introduction of a third charge, $q_3$, placed nearby.

Define the principle of superposition as it applies to electrostatic forces between multiple charges.

State Gauss's law in electrostatics.

Critique the method of charging by induction from the perspective of the law of conservation of charge.

Summarize the key differences between electrical conductors and insulators, providing one example of each.

Calculate the number of electrons that must be removed from a neutral object to give it a positive charge of $1 \mu\text{C}$.

Contrast the electrostatic force and the gravitational force with respect to their dependence on the nature of the interacting particles.

Critique the classical model of a hydrogen atom where an electron orbits a proton in a circular path, from the perspective of electromagnetic theory.

Define electric flux and state its SI unit.

Justify ignoring the quantisation of charge, $q=ne$, when dealing with macroscopic charges, for instance, a charge of $1 \mu\text{C}$.

Recall the formula for the torque experienced by an electric dipole of moment $\mathbf{p}$ placed in a uniform external electric field $\mathbf{E}$.

Define an electric dipole moment and identify if it is a scalar or a vector quantity.

Explain the property of 'quantisation of electric charge'. Why can this property be ignored when dealing with macroscopic charges?

List any three fundamental properties of electric field lines.

Explain the law of conservation of electric charge using the example of rubbing a glass rod with a silk cloth.

Summarize the expressions for the electric field due to an electric dipole at large distances for points on its axial line and for points on its equatorial plane.

Two point charges, $q_1 = +4 \mu\text{C}$ and $q_2 = -6 \mu\text{C}$, are separated by a distance of $20$ cm in a vacuum. Calculate the magnitude and direction of the electrostatic force that $q_1$ exerts on $q_2$.

Evaluate why Gauss's Law is not helpful for calculating the electric field of an electric dipole.

Three point charges are placed on the x-axis: $q_1 = +2 \mu\text{C}$ at $x=0$, $q_2 = -3 \mu\text{C}$ at $x=0.4$ m, and $q_3 = +5 \mu\text{C}$ at $x=1.0$ m. Analyze the forces acting on charge $q_2$ and calculate the net electrostatic force on it.

A spherical Gaussian surface of radius $15$ cm encloses a net charge of $5.31 \times 10^{-10} \text{ C}$. Solve for the net electric flux through the surface. How would the flux change if the radius of the surface were doubled?

An electric dipole has a dipole moment of magnitude $p = 5 \times 10^{-9} \text{ C·m}$. It is placed in a uniform electric field of magnitude $E = 4 \times 10^4 \text{ N/C}$. Calculate the magnitude of the maximum torque that the electric field can exert on the dipole.

Demonstrate how to apply Gauss's Law to find the electric field due to a uniformly charged, infinitely long straight wire. Explain your choice of the Gaussian surface and solve for the electric field at a perpendicular distance $r$ from the wire with linear charge density $\lambda$.

A uniform electric field is given by $\mathbf{E} = (200 \hat{\mathbf{i}} + 300 \hat{\mathbf{j}})$ N/C. Calculate the electric flux through a rectangular surface of area $0.1 \text{ m}^2$ lying in the yz-plane.

Analyze the properties of electric field lines to explain why they cannot form closed loops and why they never intersect.

Design an experiment using a gold-leaf electroscope to justify the claim that there are only two fundamental types of electric charges.

Justify why electrostatic field lines cannot form closed loops.

Evaluate the statement: 'The concept of an electric field is merely a mathematical construct to simplify calculations and has no true physical significance.'

Propose a method using Gauss's Law and symmetry to find the electric flux through one face of a cube that has a point charge $q$ placed at its exact center.

A neutral, insulating material can be attracted to a charged object. Justify this phenomenon using the concept of induced dipoles.

Explain the concept of 'additivity of charges' and provide a simple numerical example.

A student claims that Coulomb's Law, $F = k \frac{|q_1 q_2|}{r^2}$, is flawed because it cannot explain the stability of an atomic nucleus. Critique this statement.

A hollow conducting sphere is given a net charge of $+Q$. A point charge $+q$ is then placed inside the cavity, but not at the center. Propose the final charge distribution on the inner and outer surfaces of the sphere and justify your proposal using Gauss's Law.

Design a configuration of three point charges ($q_1, q_2, q_3$) on the vertices of an equilateral triangle of side $l$ such that the net force on one of the charges, say $q_3$, is zero.

An electric dipole consists of charges $+10 \text{ nC}$ and $-10 \text{ nC}$ separated by $2.0$ cm. Calculate the electric field at a point P located $20$ cm from the center of the dipole on its axial line. Then, compare the magnitude of this field with the field at a point Q, also $20$ cm from the center, but on the equatorial plane.

An electron with an initial velocity of zero is placed in a uniform electric field of magnitude $E = 1.5 \times 10^4 \text{ N/C}$ directed downwards. Analyze its motion and calculate its acceleration and the time it takes to travel a distance of $1.0$ cm. (Given: mass of electron $m_e = 9.11 \times 10^{-31} \text{ kg}$, charge of electron $e = -1.6 \times 10^{-19} \text{ C}$).

State Coulomb's law of electrostatics. Describe its mathematical expression in vector form for two point charges $q_1$ and $q_2$.

Three charges, $q_1 = +1 \mu\text{C}$, $q_2 = -2 \mu\text{C}$, and $q_3 = +3 \mu\text{C}$, are placed at the vertices A, B, and C respectively of an equilateral triangle of side length $10$ cm. Solve for the magnitude and direction of the net electrostatic force on charge $q_1$.

Explain why the electric field inside a uniformly charged thin spherical shell is zero. Also, describe the nature of the electric field at a point outside this shell.

Two identical metallic spheres, A and B, have charges $+4Q$ and $-2Q$ respectively. They are brought into contact and then separated to their original distance. Analyze the charge distribution after contact and calculate the ratio of the new electrostatic force to the original electrostatic force between them.

Create a problem to find the electric field from a continuous charge distribution. A semi-circular rod of radius $R$ has a uniform linear charge density $+\lambda$. Formulate the integral needed to calculate the electric field at the center of the semi-circle.

Define surface charge density. Recall its formula and calculate its value for a sphere of radius $0.1 \text{ m}$ carrying a total charge of $5 \times 10^{-6} \text{ C}$.

Propose a modification to Gauss's Law if the electrostatic force were to follow an inverse cube law, $F \propto 1/r^3$.

Formulate an expression for the net force on an electric dipole with moment $\mathbf{p} = p\hat{\mathbf{i}}$ placed in a non-uniform electric field given by $\mathbf{E} = (ax^2)\hat{\mathbf{i}}$, where $a$ is a positive constant. The dipole is centered at the origin with length $2L$.