CUET UG Physics Booster Test – 3 Conductors and Dielectrics

According to NCERT, a conductor in electrostatic equilibrium cannot have a non-zero electric field within its interior. Conductors possess a large number of free electrons. If an electric field existed inside the conductor, these electrons would experience an electrostatic force and continue to move. Such continuous motion would mean that equilibrium has not been established. When a conductor is placed in an external electric field or given excess charge, the free electrons redistribute themselves rapidly. This redistribution continues until the electric field produced by the induced charges exactly cancels the field inside the conductor. As a result, the net electrostatic field becomes zero everywhere within the conducting material. This property remains true irrespective of the shape of the conductor or the magnitude of charge placed on it. This fundamental result explains why conductors act as electrostatic shields and why the interior of a conductor remains protected from external electric influences. It is one of the most important conclusions derived in NCERT while discussing conductors in electrostatic equilibrium.

In a metallic conductor, the outermost valence electrons are weakly bound to atoms and can move freely throughout the material. Therefore, these electrons act as mobile charge carriers and are responsible for electrical conduction. The positive ions, however, remain fixed at their lattice positions and form the rigid structure of the metal. When an external electric field is applied, electrons experience a force opposite to the field direction because they possess negative charge. Consequently, the drift velocity of electrons is opposite to the direction of the electric field. Although electrons exhibit random motion due to collisions, a small average drift velocity develops. Electrostatic equilibrium is achieved when charge redistribution has completely cancelled the electric field inside the conductor. At this stage, the net electric field within the conductor becomes zero. These concepts collectively explain the behaviour of conductors and form the basis of the NCERT discussion on conductors in electrostatic equilibrium.

The electric field at the surface of a conductor in electrostatic equilibrium is always perpendicular to the surface. If a tangential component of electric field existed, free charges on the conductor would experience a force parallel to the surface and begin moving. Such movement would disturb electrostatic equilibrium. Statement 1 is correct because field lines must emerge normally from the conductor surface. Statement 2 is also correct because tangential electric fields cause charge redistribution. Statement 4 is correct since a conductor without surface charge may have zero electric field at its surface. Statement 3 is incorrect because the existence of a tangential component contradicts the condition of electrostatic equilibrium. NCERT explains that the surface of a conductor is an equipotential surface. Since electric field lines are always perpendicular to equipotential surfaces, the electric field cannot possess any tangential component. This property is fundamental in understanding charge distribution and electric field behaviour near conductors.

Gauss's law states that the total electric flux through a closed surface is proportional to the net charge enclosed within it. In a conductor under electrostatic equilibrium, the electric field inside the conductor is zero everywhere. Consequently, the electric flux through any Gaussian surface lying entirely within the conductor is also zero. Since the flux is zero, the enclosed net charge must be zero. This conclusion remains valid even if the conductor carries excess charge. The excess charge cannot remain inside the conducting material because any such charge would create an electric field and destroy electrostatic equilibrium. Therefore, all excess charge resides on the outer surface of the conductor. Statement C is incorrect because it claims that the flux inside a charged conductor is non-zero. This directly contradicts both Gauss's law and the electrostatic equilibrium condition discussed in NCERT. The result is one of the key applications of Gauss's law in understanding charge distribution in conductors.

In electrostatic equilibrium, the electric field inside a conductor is zero. Since electric field is related to the potential gradient, a zero electric field implies that there is no change in potential anywhere inside the conductor. Therefore, the entire conductor, including its surface, remains at the same potential. This result is valid regardless of the shape of the conductor. Statement 2 is therefore correct. Statement 1 is incorrect because the potential does not suddenly become zero just outside the surface; potential remains continuous across the boundary. Statement 3 is incorrect because sharper points have higher electric field strength, not higher potential. Statement 4 is incorrect because the potential need not be zero; it is simply constant throughout the conductor.

For an equipotential surface, the potential difference between any two points is zero. Since work done in moving a charge depends on potential difference, moving a charge along the surface requires no work. If a tangential component of electric field existed, it would exert a force on the charge and perform work. Therefore, in electrostatic equilibrium, the electric field must be perpendicular to the equipotential surface. Consequently, the work done in moving a charge along the surface remains zero. This is a fundamental property of equipotential surfaces discussed in NCERT.

For an electric dipole, the potential at a point depends on both distance and angle. The equatorial plane corresponds to θ = 90°, where cosθ = 0. Therefore, the potential becomes zero throughout the equatorial plane. The equipotential pattern of a dipole is symmetric with respect to the dipole axis and equatorial plane. However, unlike a single point charge, the equipotential surfaces are not concentric spheres because the potential depends on angle as well as distance. Hence statements 1 and 2 are correct, while statement 3 is incorrect.

Very close to one of the identical positive charges, the influence of that charge is much stronger than the influence of the other charge. Therefore, the potential distribution resembles the potential due to a single point charge. Since equipotential surfaces of a point charge are concentric spheres, the equipotential surfaces near each charge appear nearly spherical. At larger distances, the contributions of both charges become comparable and the equipotential surfaces become more complex.

The electric field is related to electric potential by the relation: The negative sign indicates that the electric field points in the direction in which the potential decreases most rapidly. Therefore, electric field lines always point from higher potential to lower potential. This is a fundamental link between field and potential in electrostatics and explains why equipotential surfaces are always perpendicular to electric field lines.

The magnitude of electric field is given by: Given, Therefore, Thus, the magnitude of the electric field is . Unit verification also confirms the answer because volt per metre is the SI unit of electric field.

When a conductor is placed in an external electric field, free charges redistribute themselves until the induced field exactly cancels the external field inside the conductor. Therefore statement 1 is correct. In contrast, dielectrics do not possess free charge carriers. Instead, molecules become polarized and produce an induced field opposing the applied field. This induced field reduces the net field but does not completely cancel it. Hence statements 2 and 4 are correct. Statement 3 is incorrect because complete field cancellation is a property of conductors, not dielectrics. Dielectrics only partially oppose the external field through polarization.

In a non-polar molecule, the centers of positive and negative charges initially coincide. When an external electric field is applied, these charge centers shift slightly in opposite directions. This separation creates an induced dipole moment. The displacement does not continue indefinitely because internal restoring forces arise within the molecule. Equilibrium is reached when the electric force balances the restoring force. Therefore statements A, C and D are correct. Statement B is incorrect because ordinary dielectric polarization does not imply unlimited displacement or inevitable ionization.

Polar molecules already possess permanent dipole moments even in the absence of an electric field. When an external field is applied, these dipoles tend to align themselves along the field direction. However, thermal agitation continuously disturbs this alignment. Therefore complete alignment is never achieved under ordinary conditions. The degree of polarization depends strongly on temperature because greater thermal agitation reduces alignment. Hence only statement 2 is correct, while statements 1, 3 and 4 are incorrect.

When a dielectric is placed in an external electric field, its molecules become polarized. The collective effect of all molecular dipoles is represented by the polarization vector . NCERT defines polarization as the net electric dipole moment per unit volume of the dielectric. A larger value of indicates stronger alignment of molecular dipoles and therefore stronger polarization of the material. It is not a measure of energy, charge enclosed, or permittivity ratio.

For a linear dielectric, where is polarization, is electric susceptibility, and is the applied electric field. This equation shows that polarization is directly proportional to susceptibility. Therefore, if is very large, even a small applied electric field can produce a large polarization. Electric susceptibility is thus a measure of how easily a material becomes polarized in response to an external field.

For a linear dielectric, where is polarization, is electric susceptibility, and is the applied electric field. This relation shows that polarization is directly proportional to electric susceptibility. Therefore, if the susceptibility is very large, even a small external electric field can produce significant polarization. The material becomes highly responsive to the applied field. However, unlike a conductor, the induced polarization does not completely cancel the field inside the dielectric. Instead, it merely reduces the net electric field.

In a uniformly polarized dielectric, the dipoles align in a common direction. Positive bound charges appear on one surface and negative bound charges appear on the opposite surface. Since the polarization is uniform throughout the dielectric, the contributions from neighboring dipoles cancel inside the material. Therefore, no net bound charge remains within the bulk volume. The bound charges exist only at the surfaces. Hence, the net volume charge density inside the dielectric is zero.

When a dielectric is placed in an external electric field, molecules become polarized and produce bound charges at the surfaces. These bound charges generate an electric field opposite to the applied field. The induced field originates from bound charges, not free charges, making statement 1 correct. Statement 2 is also correct because positive and negative ends of dipoles accumulate on opposite surfaces. The total electric field inside the dielectric equals the vector sum of the external field and the induced opposing field, making statement 4 correct. Statement 3 is incorrect because the induced field only reduces the applied field; it does not completely cancel it.

Polar molecules possess permanent dipole moments. When an external electric field is applied, the field exerts a torque that tends to align the dipoles along its direction. However, thermal energy continuously causes random molecular motion and opposes alignment. The final degree of polarization depends on the balance between these two effects. Stronger electric fields increase alignment, while higher temperatures increase disorder. Thus thermal energy is the primary factor opposing dipole alignment.

In a linear isotropic dielectric, the induced dipole moment develops along the direction of the applied electric field. The magnitude of the induced dipole moment is directly proportional to the field strength. Electric susceptibility is the proportionality parameter that measures how easily a dielectric becomes polarized. Linear isotropic dielectrics obey the relation , meaning polarization changes linearly with the applied field. Therefore, the correct matching is 1-b, 2-c, 3-a and 4-d.