CUET UG Physics Booster Test – 2 Conductors and Dielectrics

According to NCERT, when a conductor is placed in an external electric field, the free electrons inside the conductor experience an electrostatic force and begin to move. These charges redistribute themselves on the conductor surface in such a way that an induced electric field is produced inside the conductor. This induced field exactly opposes the applied external field. The redistribution continues until electrostatic equilibrium is established. At this stage, the resultant electric field at every point inside the conductor becomes zero. Since the given point lies inside the metallic sphere, the net electric field at that point must be zero irrespective of the magnitude of the applied external field. This property is one of the most important characteristics of conductors in electrostatic equilibrium and forms the basis of electrostatic shielding. Therefore, the electric field at a point 2 cm from the center of the conducting sphere is zero.

Free electrons in a conductor possess negative charge. Therefore, when an external electric field is applied, the electric force on the electrons acts opposite to the direction of the field. As a result, electrons drift against the applied electric field. This makes Statement 2 correct and Statement 1 incorrect. Positive ions in a metallic lattice remain fixed at their lattice positions and do not move significantly under ordinary electrostatic conditions. Hence Statement 3 is incorrect. As electrons move, they accumulate on one side of the conductor and leave a deficiency on the opposite side. This redistribution creates an induced electric field that opposes the external field. The process continues until the net electric field inside the conductor becomes zero, making Statement 4 correct. Thus, Statements 2 and 4 correctly describe the behaviour of free electrons during electrostatic equilibrium.

NCERT explains that the electric field at the surface of a conductor in electrostatic equilibrium must be perpendicular to the surface. If the field were not normal to the surface, it would possess a tangential component. A tangential electric field would exert a force on free charges present on the conductor surface. These charges would begin moving along the surface, indicating that equilibrium has not yet been achieved. Such motion would continue until the tangential component vanished completely. Therefore, the existence of a non-zero tangential component is incompatible with electrostatic equilibrium. This is why electric field lines always emerge perpendicular to the surface of a charged conductor. The requirement of zero tangential electric field is a direct consequence of the free mobility of charges in conductors.

In electrostatic equilibrium, all excess charge of a conductor resides on its outer surface. The interior volume contains no excess charge because free electrons redistribute themselves until the internal electric field becomes zero. Therefore, any small volume element inside the conductor contains zero excess charge. Likewise, a Gaussian surface drawn completely within the conductor encloses no excess charge and consequently gives zero electric flux. The outer surface is the only region where excess charge accumulates. These properties are fundamental consequences of electrostatic equilibrium and Gauss's law and are repeatedly emphasized in NCERT discussions of charged conductors. Hence the correct matching is: 1-b, 2-a, 3-c, 4-d.

Since the electric field inside a conductor at electrostatic equilibrium is zero, no work is required to move a test charge between any two points within the conductor. Therefore, Statement 1 is correct. Because the electric field is zero, the potential difference between any two points inside the conductor is also zero. As a result, the entire conductor remains at the same potential, making Statement 4 correct. Different conductors may have different constant potentials depending on their charge and surroundings, so Statement 3 is also correct. Statement 2 is incorrect because irregular shape affects charge distribution on the surface but does not create potential differences within the conductor. The conductor remains an equipotential body regardless of shape.

According to NCERT, the surface of a conductor in electrostatic equilibrium is an equipotential surface. The electric field at the surface is directed perpendicular to the surface. Since displacement along the surface is perpendicular to the electric field, the work done in moving a test charge along the surface is zero. Because the electric field inside the conductor is zero, there is no potential difference between any two points inside or on the surface of the conductor. Therefore, the potential throughout the conductor and its surface remains constant. Option B is incorrect because a normal electric field does not perform work on a charge moving tangentially along the surface. The work done depends on the component of displacement in the direction of the electric field, which is absent in this case.

NCERT derives the expression using a Gaussian pill-box surface. This relation applies generally to conductor surfaces in electrostatic equilibrium and is not restricted to spheres. Therefore, Statement 1 is incorrect. The electric field just outside a positively charged conductor is directed along the outward normal to the surface. Hence Statement 2 is correct. Since a non-zero surface charge density produces a non-zero electric field, Statement 3 is incorrect. Statement 4 is correct because any tangential component would cause free charges to move, violating electrostatic equilibrium. Therefore, the electric field must be perpendicular to the surface.

In the pill-box method used in NCERT, the Gaussian surface is chosen such that one face lies just inside the conductor and the other just outside. The electric field near the conductor surface is directed perpendicular to the surface. The curved side of the pill box has area vectors perpendicular to the electric field direction. Therefore, the angle between the electric field and the area vector is 90°, making for the side surface. As a result, the cylindrical side contributes no electric flux. Only the outer flat face contributes significantly to the total flux. This simplification allows the derivation of the important result .

When a conducting shell is placed in an external electric field, free charges redistribute themselves on the outer surface. This redistribution creates an induced electric field that exactly cancels the external field inside the conducting material. As a result, the cavity enclosed by the conductor becomes completely shielded from external electrostatic influences. The electric field inside the cavity remains zero provided no charge is present inside it. This phenomenon is known as electrostatic shielding and is discussed extensively in NCERT. It is used in practical applications such as protecting sensitive electronic equipment from external electric disturbances. Therefore, the electric field inside the hollow cavity is completely zero.

The hollow copper cube acts as an electrostatic shield. When an external electric field is applied, charges redistribute on the outer surface of the conductor. This redistribution ensures that the electric field inside the conductor and inside the charge-free cavity becomes zero. Potential difference between two points is given by the line integral of the electric field. Since the electric field inside the cavity is zero everywhere, the potential remains constant throughout the cavity region. Therefore, regardless of the distance between the points, the potential difference is zero. This result is a direct consequence of electrostatic shielding and the equipotential nature of conductor-enclosed cavities.

Dielectrics are non-conducting materials because they do not possess a significant number of free charge carriers. Unlike metallic conductors, they do not contain mobile electrons that can move freely through the material. Therefore, Statement 1 is incorrect and Statement 2 is correct. Electrolytic conductors differ from metallic conductors because charge transport in them takes place through positive and negative ions. These ions move under the influence of an electric field and produce current. Hence, Statement 3 is correct. Statement 4 is incorrect because dielectrics do not completely cancel an external electric field. Instead, their molecules become polarized, producing an induced field that opposes and reduces the external field. Complete cancellation of the field occurs inside conductors at electrostatic equilibrium, not inside dielectrics. Thus, only Statements 2 and 3 are correct.

When a dielectric is placed in an external electric field, its molecules become polarized. In non-polar molecules, induced dipole moments are developed, while in polar molecules, existing dipoles tend to align with the external field. This polarization produces bound surface charges. The field due to these induced bound charges opposes the externally applied field. However, dielectrics do not have freely moving charges like conductors. Therefore, the induced charges cannot rearrange themselves sufficiently to cancel the external field completely. As a result, the net electric field inside the dielectric is reduced but not made zero. This is the major difference between conductors and dielectrics in electrostatics. In conductors, free electrons shift until the internal field becomes zero, whereas in dielectrics, molecular polarization only weakens the field.

Non-polar molecules are those in which the centres of positive and negative charges coincide. Therefore, in the absence of an external electric field, they have zero dipole moment. When an external electric field is applied, the positive and negative charge centres get slightly displaced, producing an induced dipole moment. Polar molecules, on the other hand, already possess permanent dipole moments because their positive and negative charge centres are separated. However, in a bulk sample without an external field, these dipoles are randomly oriented due to thermal motion, so the net dipole moment of the sample is zero. When an external field is applied to a polar dielectric, the dipoles tend to align with the field. Hence the correct matching is 1-b, 2-c, 3-a, 4-d.

Polar molecules are molecules in which the centres of positive and negative charges do not coincide. Because of this permanent separation of charge centres, each polar molecule possesses a permanent electric dipole moment even in the absence of an external electric field. NCERT gives examples such as HCl and H₂O for polar molecules. In HCl, the difference in electronegativity between hydrogen and chlorine creates charge separation. In water, the bent molecular structure produces a permanent dipole moment. Statement 4 is incorrect because polar molecules do not have zero dipole moment at the individual molecular level. They possess permanent dipoles. However, in a bulk sample, the total dipole moment may be zero due to random orientation caused by thermal agitation. Therefore, Statements 1, 2 and 3 correctly describe polar molecules.

The polarisation vector P is defined as the dipole moment per unit volume of a dielectric. It describes the extent to which a dielectric material becomes polarized when placed in an electric field. Polarisation can occur in both non-polar and polar dielectrics. In non-polar dielectrics, the external field induces dipole moments by slightly separating charge centres. In polar dielectrics, permanent dipoles tend to align with the electric field. Therefore, the polarisation vector is not restricted only to non-polar dielectrics. For linear isotropic dielectrics, NCERT gives the proportionality between polarisation and electric field, showing that P increases with E. Thus, Option B is the incorrect statement.

For a linear isotropic dielectric, NCERT gives the relation , where is the polarisation vector, is the permittivity of free space, is the electric susceptibility of the dielectric medium, and is the net electric field inside the dielectric. Statement 1 is correct because directly represents electric susceptibility. Statement 3 is also correct because the field in this relation refers to the electric field inside the dielectric medium, not merely the original external field before introducing the dielectric. Statement 2 is incorrect because the simple proportionality is specifically used for linear isotropic dielectrics. Statement 4 is incorrect because in ordinary linear dielectrics, polarisation is in the direction of the electric field, not antiparallel to it.

When a rectangular dielectric slab is placed in an external electric field, its molecules become polarised. Positive and negative charges are slightly displaced, producing molecular dipoles. Inside the dielectric, neighbouring dipoles cancel each other's charges because the positive end of one dipole lies close to the negative end of the next. Therefore, any macroscopically small volume element strictly inside the dielectric contains no net charge. The unbalanced bound charges appear only at the surfaces normal to the direction of polarisation. These surface charges are called induced or bound charges. This NCERT concept explains why the interior of a uniformly polarised dielectric remains electrically neutral even though polarisation exists throughout the material. Hence, the net charge inside a small interior volume element is zero.

When a dielectric is placed in an external electric field, its molecules become polarised. This polarisation causes bound charges to appear on the surfaces normal to the applied field. These induced surface charges produce their own electric field inside the dielectric. The direction of this induced field is opposite to the external electric field. Therefore, the resultant electric field inside the dielectric is reduced. NCERT highlights this as the main distinction between dielectric behaviour and conductor behaviour. In a conductor, free charges move until the internal field becomes zero. In a dielectric, bound charges only partially oppose the external field, so the field is reduced but not fully cancelled. Thus, the unbalanced surface charges produce an internal electric field opposing the external field.

For a linear isotropic dielectric, polarisation is given by the NCERT relation: Here, is the polarisation, is the permittivity of free space, is electric susceptibility, and is the net electric field inside the dielectric. If the electric field is kept constant, then depends directly on . Therefore, when is doubled, the value of also doubles. This is a direct proportionality question based on the dielectric polarisation equation. Hence, the correct answer is Option C.

In linear isotropic dielectrics, the induced dipole moment is produced due to the displacement of positive and negative charge centres under an applied electric field. The induced dipole moment is directed along the electric field and is proportional to the field strength. Statement 1 is correct because induced dipoles align in the direction of the electric field. Statement 2 is correct because linearity means direct proportionality between induced dipole moment and electric field strength. Statement 3 is incorrect because dielectrics do not cancel the external electric field completely. They only reduce it through polarisation. Statement 4 is also incorrect because polarisation is defined for dielectric media in general and is not exclusive to polar molecules. Thus, Statements 1 and 2 correctly describe linear isotropic dielectrics.