To prevent creating kinetic energy or radiation by the test charge, the electric potential is the amount of work energy required to transport a unit of electric charge from a reference point to a specified location in an electric field with a negligible acceleration of the test charge.

The energy possessed by a body by virtue of its position relative to others is defined as the potential energy of a body. It can be influenced by other factors like electric charges and the stress experienced by them. 

The electrostatic potential in bringing a unit positive test charge from infinity to a point P against the repulsive force of another positive charge is always positive.

• Because the test charge has a force of attraction, if the charge Q is negative, the potential is also negative.
• The electrostatic potential is inversely proportional to r while the electrostatic field is inversely proportional to the square of r.

Thus, the electrostatic force on a unit charge is given by the following formula:

E = Qr2 / 4piE0rI2

An electric dipole is defined as an arrangement of two equal and opposite charges separated by distance 2a. The dipole moment is denoted by p and this is a vector quantity.

• The potential due to a dipole depends on r and the angle between position vector r and dipole moment p.
• r is the distance between the point at which potential is calculated and the midpoint of the dipole.
• Dipole potential is inversely proportional to the square of r.

Thus, the potential due to a dipole is given by the following formula:

V = 1 / 4piE0 ([qr2 - qr1] / r1r2)

The overall potential at a point owing to all the charges existing in space is equal to the sum of the individual potentials of each charge present at that point.

Thus, the potential of those charges would be:

V1 = q1 / 4piE0r,1P, V2 = q2 / 4piE0r22P, V3 = q3 / 4piE0r33P…….Vn = qn / 4piE0rnP

An equipotential surface is a surface on which the potential is the same at every point. For a single charge:

• The equipotential surfaces are concentric spherical surfaces centred at the charge because r is constant.
• For positive and negative charges, electric field lines are radial and start at or finish at the charge.

For any configuration of charges, the equipotential surface through a point is normal to the electric field present at that point.

The following can be stated according to the relation between electric field and potential:

• The electric field is in the direction of the sharpest potential drop.
• The change in the magnitude of potential per unit displacement normal to the equipotential surface at the location determines its magnitude.

Consider a moving charge travelling perpendicular from a surface B to A. The work done will be equal to the potential difference.

Potential energy reflects the current state of configuration rather than the method through which it was attained.

The potential energy for a system of charges is calculated as follows:

• The initial charge's potential energy is 0 since it is transported from infinity to a location where there are no external repulsive forces (no other charges present in space).
• Bringing another charge to the point will encounter the original charge's attractive or repulsive force, and the effort done to get it from infinity to the point will be stored as potential energy.
• Similarly, any more charges brought in from infinity will be attracted or repelled by all existing charges in the area.

When the potential energy of charge (s) is calculated in an external field, the following points are noted:

• External sources which are stationary and may be unknown, create the electric field E.
• These external sources are unaffected by the charge q.

External sources of potential energy are disregarded.

Here, the potential energy is simply the product of the charge of the particle, the potential and the product vector (r).

Here, the potential energy is simply calculated as follows:

q1V(r1) + q2V(r2) + q1q2/(4πε0r12)

In the above formula, the following are the denotations:

• r1 & r2: They are position vectors
• V(r1) & V(r2): They are external potentials at point r1 & r2

A dipole in an external field is subjected to a torque that attempts to align it with the electric field's direction. Potential energy is accumulated as a result of the work done to counteract this force.

To allow current to flow, conductors contain loosely bonded electrons. They float in the direction opposite to an external electric field. 

• Inside Conductor
• The electrostatic field inside the conductor is zero.
• The charge carriers are dispersed uniformly and there is no electric field within when there is no external electric field or static state.
• At the surface of a charged conductor
• At every location on the surface of a charged conductor, the electrostatic field is normal to the surface.
• There is a non-zero component along the normal for a non-normal electric field. As a result, in static, the electric field should have no tangential component.
• Interior of a conductor
• In the inside of the conductor, there is no electrostatic field. The extra charge is concentrated near the surface.
• Under static conditions, the extra charge accumulates on the conductor's surface. The electrostatic field is zero on a closed surface. As a result of Gauss's law, the surface does not contain any net charge.
• Throughout the volume of the conductor
• The electrostatic potential is constant across the conductor's volume and equal to its surface value.
• Because there is no tangential component in a conductor, no effort is done in the moving charge within it or on its surface. As a result, the potential remains constant.

• Dielectrics: They are non-conductive materials with a small number of charge carriers. Dipole moments are created in dielectrics by stretching and reorienting the molecules in the presence of an external electric field. The net charge on the dielectric's surface that opposes and decreases the external field is known as the collective dipole moment.
• Polarization: A molecule is produced when several atoms are linked together. These linkages or electron sharing arrangements can be polar (when electrons are distributed unequally) or non-polar (when electrons are distributed evenly).
• Depending on the charge arrangement inside the material, polar and non-polar molecules may exist.
• An external electric field can polarize a substance, resulting in the formation of an induced dipole moment within it.

Capacitor: A capacitor is a two-conductor arrangement with an insulator between them.

• A capacitor's overall charge is zero, but the conductors contain charges Q and –Q.
• With the other conductor at infinity, a single conductor can be called a capacitor.
• The charge Q is proportional to the electric field present in the area between the conductors.

Capacitance: It is denoted by C = Q/V and it depends on:

• Geometrical configuration (shape, size, separation) of the system of two conductors.
• Nature of insulator/dielectric separating

• Due to a loss in the insulating power of the intervening material, the charge on the capacitor seeps out. This occurs as a result of a larger potential difference, which results in powerful electric fields.
• Dielectric strength refers to the maximum electric field that a dielectric material can endure without breaking down and allowing charge to escape. The dielectric constant of air is 3 x 106 Vm-1.
• SI unit of capacitance is F (Farad).

A parallel plate capacitor has two big planar parallel conducting plates that are separated by a modest distance.

• Inside the capacitor, the electric field is directed from the positive to the negative plate.
• The electric field is considered uniform for extremely small d. The electric field is non-uniform for large d and bends around the plate's corners, a phenomenon known as plate fringing.

The dielectric between the plates of a parallel plate capacitor is entirely occupied by the electric field, which polarizes it. Surface charge densities are denoted by the letters σ and -σ.

When the dielectric is entirely placed between the plates of the capacitor, the capacitance rises by the factor by which it increases from its vacuum value.

Capacitors in series: The capacitors are said to be connected in series when the second plate of a capacitor is connected to the first plate of the next capacitor and so on.

• The charge across the arrangement remains the same and does not change.
• The sum of individual potential drops across each capacitor is the total potential drop.
• The sum of the inverse of individual capacitances is the inverse of the total capacitance.

Capacitors In parallel: The capacitors are said to be connected in parallel when the first and second plate of a capacitor is connected to the first and second plate of the next capacitor respectively.

• The potential across the arrangement does not change and remains the same.
• The sum of individual charges across each capacitor is the total charge.
• The total capacitance is the sum of individual capacitances.

When effort is made to transport a positive charge from the negative conductor to the positive conductor against the repulsive force, energy is stored in the capacitor.

A Van de Graaff generator is used to generate high voltages of the order of a few million volts, which results in the generation of large electric fields for experimental purposes.

1. Two charges 2 µC and -2 µC are placed at points A and B, 6 cms apart.

• Identify the equipotential surface of the system.
• What is the direction of the electric field at every point on this surface?

Solution:

• The surface over which the total potential is zero is known as an equipotential surface. The plane in the provided question is parallel to line AB. Because the magnitudes of the charges are equal, the plane is located at the midpoint of line AB.
• The direction of the electric field is normal to the plane in the direction of AB at every location on this surface.

1. Why should I refer to MSVgo's NCERT Solutions for Class 12 Physics Chapter 2?

The solutions provided in the electric potential and capacitance class 12 NCERT solutions will help clarify students’ doubts and assist them to score extremely well during exams. Students can practise the problems and calculations provided in the NCERT Solutions Class 12 Maths that can assuredly result in improved performance.

2. Is the NCERT Solutions for Class 12 Physics Chapter 2 the best reference guide for the students?

Yes, electrostatic potential and capacitance NCERT solutions are one of a kind as it provides easy-to-understand explanations of complex concepts and terms.

3. Discuss the pattern of the questions from this chapter.

This chapter is essential while preparing for competitive exams. Hence, questions from electrostatic potential and capacitance NCERT solutions will be integrated with concepts from other chapters.