Electric Charges and their Conservation

The governing concept is charge quantisation: the magnitude of charge is q = ne, where e ≈ 1.6 × 10⁻¹⁹ C. Thus n = q/e = (12.8 × 10⁻¹⁹)/(1.6 × 10⁻¹⁹) = 12.8/1.6 = 8. Because the object has positive charge, it has lost, or is deficient in, eight electrons. Therefore option A is correct; the other numbers result from incorrect division.

When identical conducting spheres touch, charge is conserved and then shared equally because both spheres have the same capacitance. Their total charge is (+10 C) + (−4 C) = +6 C. Dividing this total equally between two spheres gives +6/2 = +3 C on each. Therefore the final charge of every sphere is positive three coulombs, so option A is correct.

The governing principle is conservation of charge, followed by equal sharing among identical conductors. The total charge is (+12 C) + (−3 C) + 0 = +9 C. Since three identical spheres touch together, the total charge is divided equally: q = +9/3 = +3 C per sphere. Hence option A is correct; +9 C is the total, not each sphere’s charge.

An electron carries charge −e and a positron carries equal charge +e. Thus the initial total charge is (−e) + (+e) = 0. If the final products are neutral, their total charge is also zero, so the reaction obeys conservation of total electric charge. The process may transform matter into radiation or other products, but it cannot create a net charge. Therefore option A is correct; the other choices are not the governing principle.

Initially the system has net charge zero. Producing only one negative particle gives the final state a negative net charge, unless some unmentioned positive charge is also produced or transferred. The initial and final totals would then differ, violating the conservation of electric charge. Quantization does not repair this imbalance, and the claim does not imply anything necessary about mass or the scalar nature of charge. Therefore option A is correct.

Charge quantization states that the charge of an isolated body must be an integral multiple of e = 1.6 × 10⁻¹⁹ C. Here, Q/e = (7.2 × 10⁻¹⁹)/(1.6 × 10⁻¹⁹) = 4.5, which is not an integer. A body cannot have half of an elementary charge in this context. Positivity, the unit coulomb, and the numerical size are not the problems. Thus option A is correct.

Charging by friction involves transfer of electrons between two materials, not creation of charge. The body that loses electrons becomes positively charged, while the body that gains them becomes negatively charged. Their charges are equal and opposite if the system is isolated, so the total remains unchanged. Thus A is correct; protons are not newly created, neutrons do not simply become charged, and charge does not disappear.

Initially, the combined charge of the two neutral bodies is zero. Rubbing transfers electrons from one body to the other but does not create or destroy net charge. If the first body ends with +q, it has lost charge q; conservation therefore requires the second body to gain −q. Option A is correct. A and D violate the initial zero total, while C gives no compensating charge.

Electrostatic induction separates charges within a conductor without transferring charge to or from it, provided the conductor has no grounding or physical contact with another charged body. The induced negative and positive charges are equal in total, so they cancel algebraically and the conductor remains neutral. Hence A is correct; the signs describe local regions, not the net charge.

A body is positively charged when it has fewer electrons than required for electrical neutrality, so electron deficiency and positive net charge are valid conclusions. However, deficiency does not mean that every electron has disappeared; the body normally still contains many electrons. Thus A is the conclusion that is not certain. Options B, C, and D express the resulting imbalance correctly.

Charge conservation states that the algebraic sum of charge in an isolated system remains constant. During transfer, electrons move from one body or region to another; they are not created or destroyed. One part may become more positive and the receiving part more negative, but their changes cancel when the whole system is considered. Thus option A explains both electron transfer and unchanged total charge, whereas B and C violate conservation.

The governing principle is conservation of charge in an electrically isolated group. Touching allows charge to redistribute between the charged conductor and the neutral conductor, so the charge on each individual sphere can change. Nevertheless, if no charge enters or leaves through an external path, the algebraic sum of the charges on all bodies involved remains unchanged after every contact and separation. Therefore A is always true; the other options incorrectly describe creation, destruction, or forced neutralisation.

For identical conducting spheres brought into contact, charge is redistributed equally because the spheres reach the same electric potential under identical conditions. Charge conservation gives the total charge as −12 C, and there are four spheres. Hence charge per sphere = total charge ÷ number of spheres = (−12 C) ÷ 4 = −3 C. Option A has both the correct magnitude and sign; B ignores sharing, C reverses the sign, and D violates conservation.

Zero net charge means that positive and negative charges balance algebraically; it does not mean that the particle or object has no internal charges or cannot respond electrically. A neutral object can be polarized or experience induced charge separation in an external electric field, and it may then be attracted. Thus A is correct: its net charge remains zero in the stated sense, while electric effects can still occur. B and C make unjustified claims, and D contradicts the premise.

The governing ideas are charge conservation and equal sharing by identical conducting spheres. First calculate the total charge: 12 + (−6) + 3 = 9 coulomb. When identical spheres touch, charge redistributes until each has the same charge. Therefore each receives 9 ÷ 3 = 3 coulomb, so option A is correct. The other options either use the total charge without division or have the wrong sign or magnitude.

The governing principle is charge sharing between identical conducting spheres. When two identical spheres touch, their potentials become equal, so their total charge is divided equally. The original sphere therefore changes as follows: +24 C becomes +12 C after the first contact, +6 C after the second, and +3 C after the third. Thus option C is correct. Option A and B represent only the first and second contacts, while D does not follow equal sharing.

First, when the identical spheres touch, their total charge is conserved: (+18 C) + (−10 C) = +8 C. Equal sharing gives +4 C on each sphere. When the selected sphere is then connected to earth, it can exchange charge freely with the Earth until its potential is zero; under the usual idealized grounding assumption, its net charge becomes zero. Hence option B is correct, not the temporary +4 C value in option A.

The elementary charge is counted algebraically: gaining an electron changes charge by −e, while losing an electron changes it by +e. Starting with +7e, gaining 12 electrons gives +7e − 12e = −5e. Losing 4 electrons then adds 4e, producing −5e + 4e = −1e. Therefore option A is correct. The other choices arise from ignoring one transfer or using the wrong sign for electron gain.

Breaking a charged drop into smaller drops does not create or destroy net electric charge, so the algebraic sum of the two final charges must remain −15e. If one drop has +4e and the other has q, then q + 4e = −15e. Therefore q = −19e. Option B is correct. A value of −11e would give a total of −7e, and positive alternatives have the wrong sign and total.

A positive charge means the object has lost electrons, because electrons carry negative charge. The number lost is found from n = Q/e, using e = 1.6 × 10^-19 C. Therefore n = (2.88 × 10^-18)/(1.6 × 10^-19) = (2.88/1.6) × 10 = 1.8 × 10 = 18. Hence option B is correct; the positive sign identifies loss rather than gain.

The negative sign indicates that the particle has an excess of electrons. The magnitude of charge is related to the number of excess electrons by |Q| = ne, where e = 1.6 × 10^-19 C. Thus n = 3.84 × 10^-18 / 1.6 × 10^-19 = (3.84/1.6) × 10 = 2.4 × 10 = 24. Therefore option A is correct.

Electric charge is quantized: the charge on a free object must be q = ne, where n is an integer and e = 1.6 × 10^-19 C. For option C, q/e = (7.2 × 10^-19)/(1.6 × 10^-19) = 4.5, which is not an integer, so it cannot represent an isolated free object. Options A, B, and D correspond to −1e, +3e, and −6e and are possible.

The statement is wrong because charge on a free object must be an integral multiple of the elementary charge: q = ne. Using e = 1.6 × 10^-19 C, the magnitude gives 5.6/1.6 = 3.5, not an integer. Thus −5.6 × 10^-19 C is not an allowed isolated-object charge. Negative charge itself is valid, so A and D are false, and the coulomb is a valid unit, ruling out B.

This is charging by induction and follows charge conservation. The negative rod repels mobile electrons in the neutral conductor. While the rod is still nearby, earthing allows some repelled electrons to flow from the conductor into Earth. Removing the earth connection traps the electron deficiency; therefore, after the rod is removed, the conductor remains positively charged. It does not remain negative or neutral because the earth was disconnected first.

The governing idea is that induction requires the earth connection to be removed while the inducing rod is still present. If the rod is taken away first, its electric influence disappears, so the separated charges are no longer maintained. Because the conductor is still earthed, electrons can flow between it and Earth until the conductor reaches electrostatic equilibrium, usually becoming neutral. Thus no net permanent charge is trapped.