CBSE Class 12 Physics (2026–27)
Chapter 2: Electrostatic Potential and Capacitance
20 Important Questions & Answers
The chapter covers electric potential, potential difference, equipotential surfaces, capacitors, dielectrics, energy stored in capacitors, and combinations of capacitors as prescribed in the CBSE syllabus.
Q1. What is electric potential? How is it different from electric potential difference?
Answer:
Electric potential at a point is defined as the work done in bringing a unit positive test charge from infinity to that point against the electrostatic force without acceleration. It is a scalar quantity and its SI unit is volt (V). Electric potential difference between two points is the work done per unit charge in moving a test charge from one point to another. While electric potential refers to a single point in an electric field, potential difference refers to two points. If one joule of work is required to move one coulomb of charge between two points, the potential difference is one volt. Potential helps determine the electrical state of a point in a field.
Q2. Derive the expression for electric potential due to a point charge.
Answer:
Consider a point charge (Q). The electric potential at a distance (r) from the charge is defined as the work done per unit charge in bringing a test charge from infinity to that point. The electric field due to the charge is (E = \frac{1}{4\pi\epsilon_0}\frac{Q}{r^2}). Integrating the work done from infinity to distance (r), we obtain the potential:
[V = \frac{1}{4\pi\epsilon_0}\frac{Q}{r}]
This expression shows that electric potential is directly proportional to the charge and inversely proportional to the distance from the charge. The potential is positive for positive charges and negative for negative charges.
Q3. State any four properties of equipotential surfaces.
Answer:
Equipotential surfaces are surfaces on which every point has the same electric potential. Their important properties are:
- No work is done in moving a charge along an equipotential surface.
- Electric field lines are always perpendicular to equipotential surfaces.
- Two equipotential surfaces can never intersect each other because a point cannot have two different potentials simultaneously.
- The closer the equipotential surfaces, the stronger the electric field in that region.
Examples include concentric spherical surfaces around a point charge and parallel planes in a uniform electric field. Equipotential surfaces help visualize the distribution of electric potential in space.
Q4. Why is electrostatic force called a conservative force?
Answer:
Electrostatic force is called a conservative force because the work done by it in moving a charge between two points depends only on the initial and final positions and not on the path followed. Therefore, the work done in moving a charge around a closed path is zero. This property allows the definition of electric potential energy and electric potential. Since electrostatic forces are conservative, energy is conserved during the movement of charges in an electric field. This concept is similar to gravitational force, which is also conservative. The conservative nature of electrostatic force forms the basis for potential energy calculations in electrostatics.
Q5. Define capacitance and write its SI unit.
Answer:
Capacitance is the ability of a conductor or capacitor to store electric charge. It is defined as the ratio of charge stored on a conductor to the potential difference across it:
[C=\frac{Q}{V}]
where (Q) is the charge and (V) is the potential difference. The SI unit of capacitance is farad (F). A capacitor has a capacitance of one farad if it stores one coulomb of charge when a potential difference of one volt is applied across it. In practical applications, microfarad (μF), nanofarad (nF), and picofarad (pF) are commonly used because one farad is a very large unit.
Q6. What is a capacitor? Mention its uses.
Answer:
A capacitor is an electrical device used to store electric charge and energy in an electric field. It consists of two conductors separated by an insulating material called a dielectric. When connected to a source, equal and opposite charges accumulate on the plates. Capacitors are widely used in electronic circuits. They are used for storing electrical energy, filtering signals, tuning radio circuits, smoothing output in power supplies, and protecting circuits from voltage fluctuations. Capacitors are also used in camera flashes and memory devices. Their ability to store and release charge quickly makes them essential components in modern electronics.
Q7. Derive the capacitance of a parallel plate capacitor.
Answer:
A parallel plate capacitor consists of two large conducting plates separated by distance (d). Let the area of each plate be (A). If charge (Q) is placed on the plates, the electric field between them is:
[E=\frac{\sigma}{\epsilon_0}]
where (\sigma=\frac{Q}{A}). The potential difference between the plates is:
[V=Ed=\frac{Qd}{A\epsilon_0}]
Therefore, capacitance:
[C=\frac{Q}{V}=\frac{\epsilon_0A}{d}]
Thus, capacitance is directly proportional to plate area and inversely proportional to separation. Increasing the area increases capacitance, while increasing the distance decreases it. This relation is important for designing capacitors.
Q8. What is dielectric polarization?
Answer:
Dielectric polarization is the process in which molecules of a dielectric become aligned when placed in an external electric field. In the absence of an electric field, the positive and negative charges inside the dielectric are uniformly distributed. When an electric field is applied, these charges shift slightly in opposite directions, creating electric dipoles. This phenomenon is called polarization. Polarization reduces the effective electric field inside the dielectric material. As a result, the capacitance of a capacitor increases when a dielectric is inserted between its plates. Dielectric polarization plays a crucial role in improving the efficiency and charge-storing capacity of capacitors.
Q9. What is the effect of inserting a dielectric in a capacitor?
Answer:
When a dielectric material is inserted between the plates of a capacitor, the capacitance increases. If the dielectric constant is (K), the new capacitance becomes:
[C’=KC]
The dielectric reduces the electric field inside the capacitor due to polarization. As a result, the potential difference decreases for the same charge stored on the plates. This allows the capacitor to store more charge at the same voltage. Dielectrics also improve insulation and reduce energy loss. Materials such as mica, glass, paper, and ceramic are commonly used as dielectrics in capacitors because they significantly enhance capacitance and performance.
Q10. Distinguish between conductors and insulators.
Answer:
Conductors are materials that allow free movement of electric charges due to the presence of free electrons. Examples include copper, silver, and aluminum. In conductors, the electric field inside the material becomes zero under electrostatic equilibrium. Insulators, on the other hand, do not allow free movement of charges because their electrons are tightly bound to atoms. Examples include rubber, plastic, and glass. Insulators can become polarized in an electric field but do not conduct electricity easily. Conductors are used in electrical wiring, whereas insulators are used for protection and isolation in electrical systems.
Q11. Define potential energy of a system of charges.
Answer:
The electrostatic potential energy of a system of charges is the work done in assembling the charges from infinity to their specified positions. It represents the energy stored due to the configuration of charges. For two point charges (q_1) and (q_2) separated by distance (r):
[U=\frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r}]
The potential energy is positive for like charges because work must be done against repulsion. It is negative for unlike charges because the electric force itself performs the work. Potential energy is a scalar quantity and is measured in joules.
Q12. Explain the relation between electric field and electric potential.
Answer:
Electric field and electric potential are closely related. The electric field at a point is equal to the negative rate of change of electric potential with distance:
[E=-\frac{dV}{dr}]
The negative sign indicates that the electric field points in the direction of decreasing potential. A stronger electric field corresponds to a faster change in potential. If the potential remains constant, the electric field is zero. This relation helps determine electric field values from potential measurements and vice versa. It is widely used in electrostatics to analyze electric field distributions around charges and conductors.
Q13. Why is no work done in moving a charge on an equipotential surface?
Answer:
An equipotential surface is a surface where every point has the same electric potential. Therefore, the potential difference between any two points on the surface is zero. Since work done in moving a charge is:
[W=q\Delta V]
and (\Delta V = 0), the work done becomes zero. This means a charge can move along an equipotential surface without gaining or losing energy. The electric field is always perpendicular to the equipotential surface, so there is no component of force along the direction of motion. This property is useful in understanding the behavior of charges in electrostatic fields.
Q14. What is an electric dipole? Define dipole moment.
Answer:
An electric dipole consists of two equal and opposite charges separated by a small distance. Examples include polarized molecules and certain capacitor arrangements. The strength of a dipole is measured by its electric dipole moment, defined as:
[p=q(2a)]
where (q) is the magnitude of each charge and (2a) is the separation between them. The dipole moment is a vector quantity directed from the negative charge to the positive charge. Its SI unit is coulomb-meter (C·m). Electric dipoles play an important role in dielectric polarization and molecular physics.
Q15. What is electrostatic shielding?
Answer:
Electrostatic shielding is the phenomenon of protecting a region from external electric fields by enclosing it within a conducting shell. When a conductor is placed in an external electric field, free charges rearrange themselves on its surface so that the electric field inside the conductor becomes zero. Therefore, any object inside the conductor remains unaffected by external electric influences. Electrostatic shielding is used in sensitive electronic equipment, coaxial cables, and Faraday cages. It helps prevent interference from external electric fields and ensures accurate operation of electrical and electronic devices.
Q16. Explain capacitors connected in series.
Answer:
When capacitors are connected in series, the same charge flows through each capacitor. However, the potential difference is divided among them. The equivalent capacitance is given by:
[\frac{1}{C_s}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}]
The equivalent capacitance is always less than the smallest capacitor in the combination. Series combinations are used when a higher operating voltage is required. Although the charge remains the same on all capacitors, the voltage distribution depends on their capacitances. This arrangement is common in high-voltage electrical applications.
Q17. Explain capacitors connected in parallel.
Answer:
In a parallel combination, all capacitors are connected across the same potential difference. The total charge stored is equal to the sum of charges stored by individual capacitors. The equivalent capacitance is:
[C_p=C_1+C_2+C_3]
The equivalent capacitance is always greater than any individual capacitance in the combination. Parallel connections are used when greater charge storage capacity is needed. Since the voltage across each capacitor is the same, the total stored charge increases significantly. This arrangement is commonly used in electronic circuits requiring large capacitance values.
Q18. What is energy stored in a capacitor?
Answer:
When a capacitor is charged, electrical work is done in transferring charge from one plate to another. This work is stored as electrostatic potential energy. The energy stored in a capacitor is:
[U=\frac{1}{2}CV^2]
It can also be expressed as:
[U=\frac{Q^2}{2C}]
or
[U=\frac{1}{2}QV]
The stored energy resides in the electric field between the capacitor plates. This energy can be released when the capacitor discharges. Energy storage is one of the most important practical applications of capacitors in electrical and electronic systems.
Q19. Why is electric potential a scalar quantity?
Answer:
Electric potential is defined as work done per unit charge in bringing a test charge from infinity to a point in an electric field. Since work is a scalar quantity and charge is also scalar, their ratio is scalar. Therefore, electric potential has magnitude only and no direction. Unlike electric field, electric potential does not follow vector addition rules. Potentials due to multiple charges are added algebraically according to the principle of superposition. This scalar nature makes calculations involving multiple charges simpler than those involving electric fields.
Q20. State the importance of capacitors in everyday life.
Answer:
Capacitors are widely used in modern electrical and electronic devices because they can store and release electrical energy efficiently. They are used in power supplies to smooth voltage fluctuations, in radio and television circuits for tuning frequencies, and in camera flashes for rapid energy discharge. Capacitors are also used in computers, communication systems, electric motors, and medical equipment. In alternating current circuits, they help improve power factor and filter unwanted signals. Their ability to store charge, regulate voltage, and control electrical energy makes them indispensable in both household and industrial applications.