Electric Charges and their Conservation

Identical conducting spheres have the same size and shape, so after contact they reach equal electric potential. For identical spheres, equal potential means equal final charge. The conserved total is +6e, so each sphere receives half: +6e/2 = +3e. Thus option A is correct. The other choices either leave the charge unequal, reverse its sign, or incorrectly remove the total charge.

The relevant principle is quantization of charge. For an isolated free body, net charge is written as q = ne, where n is an integer and e is the elementary charge magnitude. Therefore a value that is not an integral multiple of e is not an allowed net charge under the usual school-level model. Option B is correct. Quantization does not mean every charge is positive or negative; the sign depends on whether electrons are gained or lost.

Charge is quantized in units of the elementary charge e, but e is extremely small, about 1.6 × 10^-19 C. A macroscopic object can contain or lose an enormous number of electrons, so its total charge changes in tiny relative steps. Those steps are normally too small to observe, making charge appear continuous. Therefore option A is correct; macroscopic objects need not be neutral, and charge certainly exists.

Rubbing transfers electrons from one material to the other. If the first object loses N electrons, it acquires charge +Ne, while the second gains those same N electrons and acquires -Ne. Thus the signs are opposite but the magnitudes are equal, provided charge exchange with the surroundings is negligible. Option A is correct. The other choices contradict charge conservation or have no physical basis.

The governing principle is conservation of electric charge: in an isolated system, charge cannot be created or destroyed, although it may move from one object or particle to another. Chemical reactions and physical processes rearrange matter and transfer electrons, but the algebraic sum of positive and negative charges remains unchanged. Therefore, option A is correct; the other options describe unrelated changes in mass, temperature, or speed.

Zero net charge means electrical neutrality, not the complete absence of charge. A body can contain positively charged protons and negatively charged electrons in equal total amounts, so their algebraic sum is zero: Q = (+Ne) + (-Ne) = 0. Thus option B is correct. Options A, C, and D incorrectly confuse net charge, which is the resultant, with the presence of individual charged particles.

An electron carries charge -e, whereas a proton carries +e and a neutron has zero electric charge. If a body has more electrons than protons, its net charge is negative; quantitatively, Q = (Nproton - Nelectron)e, which is negative when Nelectron exceeds Nproton. Hence option B is correct. Neutrons do not determine ordinary net charge, and nuclei are not the excess carriers in routine charging.

A positive net charge normally results when a body loses some electrons, while the positively charged protons remain bound in its nuclei. In terms of numbers, Q = (Nproton - Nelectron)e is positive when Nproton is greater than Nelectron. Therefore option A is correct. Protons are not ordinarily removed during rubbing or contact charging, neutrons carry no charge, and nuclei are not the deficient component.

In ordinary electrostatic charging, the mobile particles are electrons. A body becomes negatively charged when it gains electrons and positively charged when it loses them. This changes its net charge without creating or destroying charge overall; the transferred charge appears on another body. Thus option A is correct. Neutron colour, destruction of mass, and stopping time have no role in ordinary charging.

Friction can require mechanical work and may convert energy into heat, but it does not create a net electric charge from nothing. During rubbing, electrons transfer between the two materials: one becomes relatively positive and the other relatively negative. Their algebraic charges cancel when the complete system is considered. Therefore option A is correct; the total charge does not always increase or decrease, and it does not turn into mass.

Net charge is found by adding charges algebraically, including their signs. If a body has charge +Q and it is combined with an equal opposite charge -Q, then the total is Qnet = +Q + (-Q) = 0. Hence option B is correct, and the combined system becomes electrically neutral in net charge. It is not doubled, infinite, or necessarily negative; those outcomes ignore either magnitude or sign.

Conservation and quantization are different properties. Conservation states that the total charge of an isolated system remains constant, even when charge moves between bodies. Quantization states that observable charge is generally an integral multiple of the elementary charge: q = ne, where n is an integer. Therefore option A is correct. The other choices wrongly treat the principles as identical, sign-limited, or destructive.

The governing principle is conservation of electric charge. Initially both bodies are neutral, so the total charge of the isolated system is 0. After rubbing, let the first charge be −6e and the second be q. Conservation gives −6e + q = 0, so q = +6e. Therefore option A is correct. The second body must acquire an equal positive charge, not another negative or zero charge.

Use the quantisation relation Q = ne, where e is the magnitude of one elementary charge, approximately 1.6 × 10⁻¹⁹ C. The number of missing electrons is n = Q/e = (16 × 10⁻¹⁹)/(1.6 × 10⁻¹⁹) = 10. A positive charge means electrons have been removed, so the body has a deficiency of ten electrons. Hence option A is correct.

This is charging by induction. A nearby negative rod repels mobile electrons in the neutral conductor. While the rod remains nearby, earthing gives some of those electrons a path to Earth. Removing the earth connection first traps an electron deficiency on the conductor; after the rod is removed, that net deficiency remains. Therefore the conductor is positively charged, so option A is correct. The exact magnitude is not specified.

In induction, the positive rod attracts electrons toward the nearby side of the conductor. With the rod still present, earthing allows additional electrons to flow from Earth into the conductor. If the earth connection is removed first, these extra electrons remain trapped. Removing the rod afterward only redistributes them, so the conductor has a net negative charge. Thus option A is correct; no exact magnitude or doubling is implied.

A charged rod first separates charges in the conductor by electrostatic induction. If the rod is removed while the conductor is still earthed, the external influence disappears and the separated charges can flow through the earth connection until the conductor becomes neutral again. Charge is not destroyed, protons do not normally leave the lattice, and the elementary charge does not change. Therefore option A is correct.

For an internal process in an isolated system, total charge is conserved. Let Qrest be the charge on everything except the particle. Then Qrest + (−5 C) = +2 C. Therefore Qrest = +2 C + 5 C = +7 C. This positive charge balances the particle's −5 C and leaves the required total +2 C. Hence option A is correct; the other choices do not satisfy the conservation equation.

The law of conservation of electric charge requires the final total charge to equal the initial total charge, which is zero. If one created particle has charge +q, the other must have charge −q so that (+q) + (−q) = 0. A second positive or neutral particle would make the total nonzero, and a double positive charge would increase it further. Thus option A is correct.

The governing principle is conservation of electric charge. An electron has charge −e, while a positron has charge +e, so their initial total charge is (−e) + (+e) = 0. A photon is electrically neutral, so any number of photons has total charge zero. Thus photon-only production is compatible with charge conservation; charge is not destroyed or converted into an opposite sign.

Electric charge is quantized: the net charge on an isolated ordinary body is q = ne, where n is an integer and e ≈ 1.6 × 10⁻¹⁹ C. The stated value is −e/2, which would require n = −1/2, not an integer. Therefore it cannot be the net charge of an isolated body under the elementary-charge model. It is neither one-electron excess nor one-proton deficiency.

Attraction is consistent with opposite charges, but it is not exclusive to that case. A charged body can polarize a nearby neutral body by induction: opposite charge is induced closer to it, producing a stronger attractive force than the repulsion from the farther side. Therefore observing attraction alone cannot prove that both bodies are oppositely charged. Repulsion, in contrast, is a much more definite sign of like charges.

Under the school-level quantization rule, the charge of an isolated observable body is written as q = ne, where n is an integer and e is the elementary charge. A value of +(2/3)e is not an integral multiple, so it does not fit the usual rule for an isolated object. Therefore option A is the intended answer. Quarks can have fractional charges in advanced particle physics, but that nuance does not change the stated school-level interpretation.

Charge quantization requires the charge of an isolated body to be q = ne, where n is an integer and e ≈ 1.6 × 10⁻¹⁹ C. For the stated value, q/e = (7.2 × 10⁻¹⁹)/(1.6 × 10⁻¹⁹) = 7.2/1.6 = 4.5. Since 4.5 is not an integer, the value is doubtful under the school-level rule. Thus option A is correct; positivity and the unit coulomb are not problems.

Charge conservation states that the algebraic total charge of an isolated system remains constant, while charge quantization states that charge occurs in integral multiples of the elementary charge e. If a problem asks for both the final total charge and the number of electrons, conservation determines the net balance and quantization gives N = |Q|/e. Therefore option A requires both ideas; the other choices concern unrelated physical quantities.