CUET UG Physics Booster Test – 3 Material Properties and Coulomb’s Law

According to NCERT, ordinary macroscopic objects contain an extraordinarily large number of charged particles. A copper cube of side 1 cm has a volume of 1 cm³ and contains roughly 10²² atoms. Since each copper atom contains 29 electrons, the total number of electrons present becomes approximately 2.5 × 10²⁴. This includes both bound electrons and conduction electrons. This large value illustrates why matter is electrically neutral under normal conditions despite containing huge amounts of positive and negative charges. Electrostatic phenomena arise due to the transfer of only a tiny fraction of these electrons. The result also highlights the microscopic basis of charge and the enormous number of charge carriers present in conductors. Therefore, the correct answer is 2.5 × 10²⁴ electrons.

NCERT explains that insulators do not contain free electrons capable of moving throughout the material. When an insulator such as glass, rubber or plastic is rubbed, charge transfer occurs due to friction. Since charges cannot move freely, the acquired charge remains localized near the rubbed region. This localized charge retention is responsible for many electrostatic phenomena such as attraction of paper bits by a charged comb and charging of plastic rods. Statements 1 and 2 correctly describe the behavior of insulators. Statements 3 and 4 are incorrect because rapid charge migration and instant grounding require mobile charge carriers, which are absent in insulators. Hence only Statements 1 and 2 are correct.

According to NCERT, when excess charge is placed on a conductor, free electrons move under mutual repulsion until electrostatic equilibrium is established. As a result, excess charge resides on the outer surface of the conductor. The electric field inside a conductor at electrostatic equilibrium is zero. If any field existed, free charges would continue moving. Therefore, the existence of zero internal electric field is a defining characteristic of electrostatic equilibrium. Thus: 1 → b 2 → d 3 → c 4 → a The matching reflects the fundamental properties of conductors discussed in NCERT.

NCERT explains that insulators do not permit free movement of charge. Consequently, charges produced by friction remain trapped at localized positions. This localization allows static electricity to persist for long periods. The attraction of paper pieces by a charged comb and charging of plastic objects are common examples. Because charges cannot move freely, localized charges do not rapidly neutralize one another unless a conducting path is provided. Therefore, Statement B is incorrect. The other statements correctly describe the behavior of static charge on insulating materials and agree with NCERT discussions of frictional electricity.

Earthing is the process of connecting a charged body to the earth through a conducting path. NCERT treats the earth as a vast reservoir capable of accepting or supplying charge without appreciable change in its electrical state. Therefore, excess charge can flow through a conducting connection to the ground. The human body behaves as a conductor because it contains water and dissolved ions. Hence a charged metal rod held directly by hand often loses its charge through the body to the earth. To prevent this, insulating handles made of wood or plastic are used. These materials interrupt the conducting path and reduce leakage. All four statements correctly describe the process of grounding and earthing.

According to NCERT, the earth behaves as an enormous reservoir of electric charge. When a charged conductor is connected to the earth through a conducting path, excess charge flows between the conductor and the earth until electrostatic equilibrium is established. A barefoot human standing on the ground provides such a conducting path because the body contains water and dissolved salts, making it a conductor. Therefore, when a charged metal sphere is touched, the excess charge leaks through the body to the earth. In the idealized NCERT treatment, all excess charge is removed from the sphere and transferred to the earth. Hence the final charge on the sphere becomes zero. Therefore: Final charge = Q − Q = 0 Thus Option C is correct.

NCERT defines a point charge as a charged body whose dimensions are negligible compared with the distance involved in the interaction. For the first pair of spheres, r is not much larger than R. Therefore, the size of the spheres cannot be ignored and the point charge approximation becomes invalid. For the second pair, d >> R. The sphere dimensions are negligible compared with the separation distance. Consequently, each sphere may safely be treated as a point charge. This distinction is important because Coulomb's law is strictly applicable to point charges. Extended charge distributions require more advanced treatment when object size becomes comparable to separation. Hence the correct classification is: Not point charges, Point charges.

The point charge concept is one of the most useful idealizations in electrostatics. According to NCERT, a point charge is a charged body whose size is negligible compared to the distance of interest. This allows Coulomb's law to be applied using simple geometry instead of dealing with complicated charge distributions. The model assumes that the entire charge content is concentrated at a single point in space. Therefore Statements 1 and 2 are correct. Statement 4 is also correct because many microscopic interactions involving elementary particles are modeled successfully using point charges. Statement 3 is incorrect because when two charged spheres touch each other, their finite sizes become important. In such situations, the point-charge approximation is no longer valid. Hence Statements 1, 2 and 4 are correct.

NCERT states that electric charge is a scalar quantity. However, unlike mass, charge may be positive or negative. Therefore, while determining the net charge of a system, algebraic signs must always be taken into account. For example, a charge of +5 C and a charge of −3 C combine to produce a net charge of +2 C. Simply adding magnitudes would produce an incorrect result. Charge addition follows ordinary algebraic rules rather than vector addition. The sign indicates the nature of the charge and determines whether charges reinforce or partially cancel one another. Therefore, the correct statement is that proper positive and negative signs must be used during charge summation.

NCERT distinguishes clearly between scalar and vector quantities. A vector quantity possesses both magnitude and direction, whereas a scalar quantity possesses only magnitude. Electric charge is a scalar quantity because it does not have any spatial direction associated with it. Coulomb force, however, is a vector because it acts along the line joining two charges and has both magnitude and direction. Therefore: 1 → c (Vector quantity → Has magnitude and direction) 2 → b (Scalar quantity → Electric charge) 3 → d (Coulomb force → Electrostatic interaction force) 4 → a (Net charge → Total charge of a system) This matching correctly reflects the NCERT treatment of charge and force.

According to NCERT, the algebraic sum of charges in an isolated system remains constant. This is the law of conservation of charge. While certain elementary particles may be created or annihilated in high-energy processes, the total charge before and after the process remains unchanged. Electrons can move from one body to another during charging by friction, conduction or induction. However, such transfer does not alter the net charge of the isolated system. Statement 4 is incorrect because charge conservation is a universal law and remains valid even during nuclear and particle interactions. Numerous experiments confirm that total charge remains unchanged in all known physical processes. Therefore, Statements 1, 2 and 3 are correct.

NCERT emphasizes that electric charge is conserved in every physical process. During beta decay, a neutron transforms into a proton, an electron and an antineutrino. Before decay: Net charge = 0 After decay: Proton = +e Electron = −e Antineutrino = 0 Total charge = +e − e = 0 Thus, the total charge after decay remains equal to the initial charge. No net positive charge is created. This provides strong experimental evidence for the conservation law. Therefore, the statement claiming that nature creates a net positive charge during beta decay is incorrect.

Number of water molecules: N = (250/18) × (6.02 × 10²³) ≈ 8.36 × 10²⁴ Each H₂O molecule contains 10 protons. Total protons: = 10 × 8.36 × 10²⁴ = 8.36 × 10²⁵ Total positive charge: Q = Ne = (8.36 × 10²⁵)(1.6 × 10⁻¹⁹) ≈ 1.34 × 10⁷ C Unit Verification Number of charges × charge per proton = Coulomb This enormous value demonstrates that ordinary matter contains huge amounts of positive and negative charge, which cancel each other to produce electrical neutrality. Therefore, Option A is correct.

At microscopic scales, the number of charge carriers may be very small. In such situations, charge quantization becomes important. NCERT states that charge exists only in integral multiples of the elementary charge e. When only a few electrons are present, charge appears as distinct, countable units rather than a continuous quantity. Therefore Statements 1, 2 and 3 are correct. Statement 4 is incorrect because the continuous approximation is mainly useful for macroscopic systems containing enormous numbers of elementary charges. The microscopic world reveals the discrete nature of charge very clearly, a fact established experimentally through Millikan's oil-drop experiment.

In SI units, electric charge is defined in terms of electric current. One coulomb is the amount of charge transported by a current of one ampere in one second. Using Coulomb's law: F = kq₁q₂/r² For q₁ = q₂ = 1 C and r = 1 m, F = 9 × 10⁹ N Therefore Statement 2 is correct. In practical electrostatics, charges are usually of the order of microcoulombs or millicoulombs because one coulomb is a very large quantity of charge. Hence Statement 4 is correct. Statement 3 is omitted from the correct set because the intended NCERT emphasis is on practical usage rather than simply calling the unit "large."

According to NCERT, the charge on a single electron is: e = 1.6 × 10⁻¹⁹ C Since an electron carries negative charge, its charge is represented as −e. If a system contains N electrons, the total charge is obtained by multiplying the number of electrons by the charge carried by each electron: Q = N(−e) Q = −Ne The negative sign indicates an excess of electrons in the system. This relation is fundamental to the quantization of charge and is widely used in electrostatics, current electricity and atomic physics. Thus, the correct expression for the total charge is −Ne.

Coulomb's experiments showed that the electrostatic force between two stationary point charges depends inversely on the square of the distance separating them. This relationship is expressed mathematically as: F ∝ 1/r² Combining this result with the dependence on charge magnitudes gives Coulomb's law: F = k(q₁q₂)/r² This inverse-square dependence is similar to Newton's law of gravitation. It implies that doubling the distance reduces the force to one-fourth, while halving the distance increases the force four times. The experimental verification of this law using a torsion balance was one of the most important achievements in electrostatics and forms the foundation of the chapter.

NCERT compares the electric and gravitational forces between elementary particles to demonstrate the relative strength of the electromagnetic interaction. For an electron-proton pair: Fe/Fg ≈ 2.4 × 10³⁹ For a proton-proton pair: Fe/Fg ≈ 1.3 × 10³⁶ These extremely large ratios show that electrostatic forces are many orders of magnitude stronger than gravitational forces at atomic scales. This is why atomic and molecular structures are governed primarily by electromagnetic interactions rather than gravity. The result also highlights the importance of Coulomb's law in explaining microscopic physical phenomena. Therefore, Option B is correct.

Coulomb's torsion balance experiment was designed to determine how electrostatic force depends on charge and distance. The experiment used charged conducting spheres attached to a sensitive torsion balance. A major strength of the method was that Coulomb did not need to know the exact magnitude of the charges initially present. Instead, he used identical conducting spheres to divide charge into predictable fractions through contact. This allowed him to compare forces corresponding to different charge values. The experiment successfully established the inverse-square law of electrostatic force. Therefore, the statement that Coulomb started with precisely known absolute charge magnitudes is incorrect. Hence Option C is the correct answer.

Using Coulomb's law: F = kq₁q₂/r² Given: k = 9 × 10⁹ N m² C⁻² q₁ = q₂ = 1 μC = 10⁻⁶ C r = 1 cm = 10⁻² m Substituting: F = (9 × 10⁹)(10⁻⁶)(10⁻⁶)/(10⁻²)² = (9 × 10⁹)(10⁻¹²)/(10⁻⁴) = 9 × 10⁻³ × 10⁴ = 90 N Unit Verification (N m² C⁻²)(C²)/m² = N Therefore, the electrostatic force between the two charges is 90 N. Hence Option A is correct.