Practice Questions

Recall the expression for the potential energy of a system of two point charges $q_1$ and $q_2$ separated by a distance $r$.

A parallel plate capacitor has a capacitance of $20 \mu\text{F}$ in air. Recall the relevant formula and calculate the new capacitance if the space between its plates is completely filled with a dielectric material of dielectric constant $K=4$.

Define electrostatic potential at a point in an electric field.

Justify why the net work done by an electrostatic field in moving a charge along any closed loop is always zero.

Recall the name of the physical quantity whose SI unit is the farad (F).

Analyze the work done by the electric field when a charge of $+5 \mu\text{C}$ is moved from a point A to a point B on the same equipotential surface.

Propose a simple modification to a parallel plate capacitor that would double its capacitance without changing the plate area or the material between the plates.

Define the dielectric constant of a substance in terms of capacitance.

Examine why the electrostatic potential is constant throughout the volume of a conductor and has the same value on its surface.

Summarize the expressions for the equivalent capacitance when 'n' capacitors with capacitances $C_1, C_2, \ldots, C_n$ are connected in (a) series and (b) parallel.

Two capacitors of capacitances $C_1 = 3 \text{ pF}$ and $C_2 = 6 \text{ pF}$ are connected in parallel to a $100 \text{ V}$ supply. Calculate the charge on each capacitor.

Examine the magnitude of the electric field between two parallel equipotential surfaces separated by $2 \text{ cm}$ if their potential difference is $10 \text{ V}$.

Propose a reason why equipotential surfaces can never intersect each other.

You are given three identical capacitors, each with a capacitance of $C = 9 \text{ pF}$. Create two different network configurations using all three capacitors that result in different equivalent capacitances and calculate the value for each proposed design.

Explain the phenomenon of electrostatic shielding.

Evaluate the safety of a person inside a metal-bodied car during a lightning strike. Justify your answer using the concept of electrostatic shielding.

Recall the formula for the capacitance of a parallel plate capacitor and list the factors on which it depends.

Describe the difference between polar and non-polar molecules with one example for each.

List three fundamental properties of an equipotential surface.

Explain the relationship between electric field and electrostatic potential at a point.

Recall the formula and calculate the electrostatic potential at a point P, located $15$ cm away from a point charge of $3 \times 10^{-7} \text{ C}$. (Take the value of $\frac{1}{4\pi\varepsilon_0}$ as $9 \times 10^9 \text{ Nm}^2\text{C}^{-2}$)

Calculate the electrostatic potential at a point P, which is equidistant at $10 \text{ cm}$ from two charges, $q_1 = +2 \times 10^{-8} \text{ C}$ and $q_2 = -4 \times 10^{-8} \text{ C}$, if the distance between the charges is $12 \text{ cm}$.

A parallel plate capacitor is charged by a battery and remains connected to it. A dielectric slab with dielectric constant $K$ is then inserted between its plates. Analyze how the (i) capacitance, (ii) charge on the plates, and (iii) energy stored in the capacitor change.

An electric dipole consists of charges $\pm 2 \times 10^{-8} \text{ C}$ separated by a distance of $2 \text{ mm}$. Solve for its potential energy when it is placed in a uniform electric field of $5 \times 10^4 \text{ N/C}$ at an angle of $30^\circ$ with the field.

Apply the formula for a parallel plate capacitor to calculate the area of the plates required to construct a $2 \text{ F}$ capacitor, if the plates are separated by a $0.5 \text{ mm}$ thick paper sheet with a dielectric constant $K=4$. (Permittivity of free space $\varepsilon_0 = 8.85 \times 10^{-12} \text{ F/m}$).

Contrast the behavior of a conductor and a dielectric material when each is placed in a uniform external electric field. Use diagrams to demonstrate the resulting electric fields.

Two point charges, $q_1 = 4 \mu\text{C}$ and $q_2 = -1 \mu\text{C}$, are separated by a distance of $30 \text{ cm}$. Solve for the point on the line joining the two charges where the electric potential is zero, assuming the potential at infinity is zero.

A student claims that inserting a conducting slab of thickness $t$ (where $t < d$) between the plates of an isolated parallel plate capacitor (separation $d$, area $A$) will increase its capacitance. Evaluate this claim by formulating an expression for the new capacitance.

Explain why the electrostatic potential is constant throughout the volume of a conductor and has the same value on its surface.

A parallel plate capacitor is charged by a battery and then disconnected. A dielectric slab is then inserted between the plates. Evaluate the change in (i) the charge on the plates, (ii) the potential difference, and (iii) the energy stored in the capacitor. Justify your reasoning.

Critique the statement: 'The electrostatic potential energy of a system of two point charges is always positive.' Justify your critique with physical reasoning for both like and unlike charges, and formulate the general expression for potential energy.

Two concentric spherical conducting shells have radii $r_1$ and $r_2$ ($r_2 > r_1$) and carry charges $Q_1$ and $Q_2$ respectively. Formulate an expression for the potential at a point at a distance $r$ from the center, where $r_1 < r < r_2$. Justify each term in your expression.

Evaluate the statement: 'For a system of two point charges, the potential is zero somewhere on the line joining them.' Critique this statement and identify the specific conditions under which it could be true.

A student argues that since the electric field inside a conductor is zero in an electrostatic situation, the electric potential must also be zero inside. Critique this argument and justify the correct relationship between electric field and potential inside a conductor.

Compare the dependence of electrostatic potential on distance $r$ for a single point charge and for an electric dipole at large distances ($r \gg$ size of dipole). Analyze the reason for this difference.

Analyze why the net electric field inside the bulk of a conductor must be zero in a static situation, even when it is placed in an external electric field.

Calculate the work required to assemble a system of three charges: $q_1 = +1 \mu\text{C}$ at $(0,0)$, $q_2 = -2 \mu\text{C}$ at $(3 \text{ cm}, 0)$, and $q_3 = +4 \mu\text{C}$ at $(0, 4 \text{ cm})$.

Design a capacitor system with an equivalent capacitance of $2 \mu\text{F}$ using the minimum number of available $3 \mu\text{F}$ capacitors. Draw the circuit diagram and justify your design by calculation.

Formulate a method to calculate the work done in assembling a system of four equal charges, $q$, at the vertices of a regular tetrahedron of side length $a$. Derive the final expression for the total potential energy of this configuration.

Describe the principle of a capacitor and explain why its capacitance increases when a dielectric slab is introduced between its plates.

A $400 \text{ pF}$ capacitor is charged by a $100 \text{ V}$ battery. After disconnecting the battery, it is connected to another uncharged $400 \text{ pF}$ capacitor. Calculate the electrostatic energy lost in this process.

A capacitor of capacitance $C$ is charged to a potential $V$. The charging battery is then disconnected, and the capacitor is connected to an identical uncharged capacitor in parallel. Formulate an expression for the loss of energy in this process and justify why energy is not conserved, proposing where the 'lost' energy goes.

Summarize the process of charging a capacitor and derive the expression for the energy stored in it, $U = \frac{1}{2}CV^2$.

Design an experiment to determine the dielectric constant of a liquid. You are provided with a parallel plate capacitor, a battery of known voltage $V$, and a charge measuring device (electrometer). Justify the steps and formulate the equation to calculate the dielectric constant $K$.

Solve for the equivalent capacitance and the total charge stored in the network shown below, connected to a $12 \text{ V}$ supply. The capacitors have capacitances $C_1 = 2 \mu\text{F}$, $C_2 = 4 \mu\text{F}$, and $C_3 = 6 \mu\text{F}$. $C_1$ and $C_2$ are in series, and this combination is in parallel with $C_3$.