Electric Charges and their Conservation

In a conductor, excess charge carriers are mobile. If excess charge remained distributed through the bulk, their mutual repulsion and the resulting internal electric field would drive them to move. They continue redistributing until electrostatic equilibrium is reached, at which point the electric field inside the conducting material is zero and excess charge resides on the surface. Hence the bulk volume charge density is taken as zero, although surface charge density can be nonzero.

When two conducting spheres are connected, mobile electrons redistribute until both spheres reach the same electric potential. For identical spheres, equal potential corresponds to equal charge because their capacitances are equal. If the total charge is Q, the final charge on each sphere is Q/2. Thus A is correct; charge is conserved, masses do not need to change, and protons do not escape.

When two bodies are rubbed, electrons may transfer from one surface to the other, but electric charge is not created or destroyed. If one body loses charge q, the other gains charge of equal magnitude and opposite sign, so the algebraic total remains unchanged: q + (−q) = 0. Therefore option A is correct. The other conservation laws concern energy, momentum or mass, not this charge-transfer result.

Electric charge is quantised according to q = ne, where e is the magnitude of the elementary charge and n is the number of excess or missing electrons. A negative charge means electrons have been added. Here |q| = 7e, so n = |q|/e = 7e/e = 7. Therefore the body has seven extra electrons, making option A correct; six, eight and fourteen do not satisfy the stated charge.

This is charging by conduction. A negatively charged rod contains an excess of mobile electrons. When it touches the neutral metal sphere, some electrons move through the contact into the sphere until electrical equilibrium is reached. The sphere then has more electrons than protons and therefore a negative net charge. Protons and neutrons do not normally transfer or form in this process, so option A is the only valid explanation.

A positive rod has an electron deficiency and attracts mobile electrons. On direct contact with the neutral conductor, electrons flow from the conductor toward the rod until the potential difference is reduced. The conductor loses electrons, so it is left with a positive net charge. Option B would make the conductor more negative, option C requires an earth connection not stated here, and option D contradicts conduction.

Attraction alone does not establish that the paper has an opposite net charge. If the paper is neutral, the electric field of the charged body can polarize it: opposite charge is induced closer to the body and like charge is displaced farther away, producing a net attraction. Therefore option A cannot be concluded with certainty. Options B and C describe possible polarization, while D follows from the observed electric interaction.

During charging by induction, a nearby charged body separates the mobile charges in a conductor without touching it. Earthing connects the conductor to the large Earth, which can supply electrons or accept excess electrons while the inducing body is present. After the earth connection is removed and then the inducing body is taken away, the conductor can retain a net charge. Earthing therefore provides a charge-transfer path; it does not destroy charge or change the conductor into an insulator.

The governing concept is charging by induction with earthing. A nearby negative rod repels mobile electrons in the conductor. If the conductor is earthed, some electrons leave it; disconnecting the Earth first and then removing the rod prevents their return. The conductor is left with an electron deficiency, so its net charge is positive, making option A correct. Option B reverses the effect, while C and D ignore the net charge produced by the procedure.

The governing idea is induction accompanied by earthing. A positive rod attracts electrons toward the conductor’s nearby side. While the rod remains near, electrons flow from Earth into the conductor. If the Earth connection is removed first and the rod is then taken away, these extra electrons remain distributed over the conductor, giving it a net negative charge. Hence option A is correct; B is the result associated with a negative rod, whereas C and D incorrectly claim that no net charge remains.

The elementary charge magnitude is e = 1.6 × 10⁻¹⁹ C. The number of missing electrons is calculated using n = Q/e. Here n = (1.6 × 10⁻¹⁹)/(1.6 × 10⁻¹⁹) = 1. The positive sign indicates that one electron is missing, not that a positive particle was created. Therefore option A is correct; two and ten would give larger charge magnitudes.

Use the quantization relation Q = ne, where e = 1.6 × 10⁻¹⁹ C is the magnitude of the charge on one electron. Thus n = |Q|/e = (3.2 × 10⁻¹⁹)/(1.6 × 10⁻¹⁹) = 2. The negative sign means these are extra electrons rather than missing electrons. Therefore option A is correct; one, three, and four would produce different charge magnitudes.

Electric charge is quantized, meaning the charge on an isolated body must be Q = ne, where n is an integer and e is the elementary charge. Values such as 0, +4e, and −3e are allowed because their multipliers are integers. The value 2.5e is not allowed in this school-level model because 2.5 is not an integer. Therefore option A is the impossible charge.

Electric charge is a signed scalar quantity, so its algebraic sign must be retained when charges are combined. For example, +5 C and −3 C give a net charge of +2 C, whereas adding magnitudes would incorrectly give 8 C. Opposite charges can cancel partly or completely; therefore option A is correct. The other choices deny charge addition, wrongly claim all charge is positive, or deny that charge has magnitude.

The governing rule is algebraic addition of charge, including each sign. Thus q_net = (+2 C) + (−5 C) + (+1 C). First, +2 C + +1 C = +3 C; then +3 C − 5 C = −2 C. Therefore option A is correct. Positive 8 C results from ignoring the negative sign, +2 C reverses the sign or arithmetic, and zero is not obtained from these values.

Charge conservation states that the net charge of an isolated system cannot change. When conducting spheres touch, mobile charge may redistribute between them until electrostatic equilibrium is reached, but charge is not created or destroyed. Hence the sum q1 + q2 is the same before and after contact. The individual charges need not remain equal or unchanged, so options B and C are not guaranteed; D contradicts conservation.

The conservation law involved is conservation of electric charge: the algebraic total charge before a process must equal that after it. If the initial state has zero net charge, producing a positive particle with charge +q and a negative particle with charge −q gives (+q) + (−q) = 0. Their masses and motion are separate issues, so options B, C, and D do not explain the pairing. Therefore A is correct.

The elementary charge has equal magnitude e for a proton and an electron, but their signs are +e and −e. Adding one of each gives q_net = (+e) + (−e) = 0. Thus the pair is electrically neutral in net charge, although the particles still exist and may interact electrically. Options B and C ignore one sign, while D incorrectly adds magnitudes instead of signed charges. Hence A is correct.

A neutral atom initially has equal numbers of protons and electrons, so its net charge is zero. Removing one negatively charged electron leaves one excess positive elementary charge: q_net = (+Ze) + [−(Z−1)e] = +e. The nucleus does not become a neutron, and the atom does not remain neutral. Therefore it becomes a cation, or positive ion, making option A correct.

A neutral atom has equal positive and negative charge, so its initial net charge is zero. Adding one electron adds an elementary charge −e without adding a proton; consequently q_net changes from 0 to −e. The atom therefore becomes an anion, or negative ion. It cannot become positive or remain neutral, and an electron does not turn into a proton merely by being added. Hence option A is correct.

A scalar quantity is described by magnitude and has no spatial direction. Electric charge is scalar, while its positive or negative sign identifies the two types of charge and determines algebraic addition and attraction or repulsion. The sign is therefore not a vector direction, velocity, or mass indicator. For example, +q and −q are opposite charge types, and their sum may be zero. Thus option A is correct.

Earthing is explained by charge conservation and the conducting nature of the Earth. Earth is an enormous charge reservoir, so when a charged conductor is connected to it, electrons can flow from the conductor to Earth or from Earth to the conductor. The flow continues until electrical equilibrium is reached, often leaving the conductor neutral. Charge is transferred, not destroyed; protons and neutrons do not explain this process.

The relevant principle is quantisation of electric charge. For ordinary observable bodies, charge is expressed as q = ne, where n is an integer and e is the elementary charge. Consequently, a measured charge that is not an integral multiple of e is doubtful, unless an unusual measurement or physical context is being considered. Conservation concerns whether total charge changes; it does not explain the integral-multiple condition, so option A is correct.

When two conducting bodies touch, electrons may move between them, so the charge on each individual body can change. However, if the pair is treated as an isolated system, no net charge enters or leaves it. Thus the algebraic sum q1 + q2 before contact equals q1 + q2 after separation. The individual charges need not remain fixed, and temperature or colour is not the conserved quantity asked for. Hence A is correct.

A reliable method uses two governing ideas. First, net charge is an algebraic sum, so positive and negative signs must be retained while adding charges. Second, charge quantisation requires the result, when appropriate, to be an integral multiple of the elementary charge e. Ignoring signs can reverse the answer, and assuming zero charge or positive electrons contradicts basic definitions. Therefore option A is the safest procedure.