Electric Charges and their Conservation

The charge relation q = ne gives q = -2e in this case. The negative sign means the body has an excess of negative charge, and the magnitude 2e means two elementary charges. In ordinary matter, this corresponds to two additional electrons relative to the number of protons. Two extra protons would give positive charge, losing one electron gives +e, and half an electron is not allowed by charge quantization. Therefore A is correct.

Using the quantization expression q = ne, setting n = 0 gives q = 0e = 0. Thus the body is neutral in net charge, meaning its total positive and negative charges cancel. This does not mean that the body contains no particles; atoms and charged particles may still be present internally. Options B and C contradict the zero net value, while D confuses electrical neutrality with absence of matter.

The governing law is conservation of electric charge. A closed system does not exchange net charge with its surroundings. Internal processes, such as separation, transfer, or recombination of charges, can change the charge of individual parts but cannot change their algebraic sum. Therefore the final total remains +3 C, so option A is correct. Zero, −3 C, or 6 C would require an unaccounted external transfer or an invalid change in the conserved total.

Use conservation of charge. Initially, the system has net charge 0. If one body acquires charge −5e, where e is the elementary charge, the other body must acquire q such that q + (−5e) = 0. Hence q = +5e. Option A is correct. A second negative charge would make the total −10e, zero would leave −5e, and +10e would make the total +5e, so those distractors violate the stated initial net charge.

The governing concept is electrostatic repulsion between like charges. Charge supplied to or induced in an electroscope spreads through its conducting stem and reaches both leaves. The two leaves consequently acquire charges of the same sign, and Coulomb repulsion pushes them apart, producing divergence. Therefore option A is correct. Opposite charges would attract rather than separate, while temperature and mass changes are not the direct electrical cause of the observed motion.

The governing concept is charging by conduction. When the charged body touches the electroscope’s metal terminal, mobile electrons move between the two bodies until their potentials adjust. The transferred charge spreads through the stem to both leaves, giving them charges of the same sign; their mutual repulsion makes them diverge. Thus option A is correct. Mass transfer is not the relevant observation, heat is not destroyed, and a neutral electroscope would not show this charge-driven divergence.

The governing principle is conservation of electric charge: charge is neither created nor destroyed in an ordinary charging process. Usually, electrons are transferred from one body to another, while protons remain bound inside atomic nuclei. A neutral body becomes charged because it has an excess or deficiency of electrons, so option A is correct. Options B and C incorrectly suggest that new particles are produced, and D confuses charging with creation of mass.

When glass is rubbed with silk, electrons move from the glass to the silk. The glass therefore loses negative charge and becomes positive, while silk gains the same number of electrons and becomes negative. By charge conservation, the charges produced on the two bodies are equal in magnitude and opposite in sign, so option A is correct. The other choices violate this conservation-based transfer.

A negative ebonite rod has gained electrons during rubbing. Those electrons must have come from the wool, because ordinary frictional charging transfers electrons rather than creating them. Losing electrons leaves wool with a net positive charge. Thus option A is correct. Wool does not become negative, remain neutral, or automatically return to zero merely because the rubbing has ended; its final charge is positive if leakage is neglected.

A body’s net charge is the algebraic sum of its positive and negative charges. A negative body generally contains both protons and electrons, but it has more electrons than the number required for neutrality. The protons remain in atomic nuclei and are not removed in ordinary charging. Therefore option A is correct; negative charge means electron excess, not absence of protons or mass.

Positive charge means that the body has a deficit of electrons relative to its neutral state; it does not mean that every electron has disappeared. The body still contains electrons and protons, but the positive charge of its protons slightly exceeds the negative charge of its electrons. Hence option A is correct. Options B and C incorrectly describe complete removal of electrons, while D ignores charged particles.

Electrons carry negative charge, whereas protons carry positive charge and normally remain fixed inside nuclei. If some electrons are removed from a neutral body, its remaining positive charge exceeds its negative charge, giving it a net positive charge. Thus option A is correct. Adding electrons would make the body negative, while adding neutrons or changing colour does not produce the required net electric charge.

The charge of an electron is negative. Therefore, when extra electrons are transferred onto a body, the negative charge exceeds the positive charge of its protons and the body acquires a net negative charge. Option A is correct. Removing electrons would produce positive charging, while simply changing volume does not alter the total charge; adding protons is not the usual process for ordinary material bodies.

The governing concept is the interaction rule for electric charges: like charges repel one another, whereas unlike charges attract one another. Therefore, when a question asks whether the force between two charged bodies is attractive or repulsive, this rule gives the answer immediately. Temperature, length, and colour are physical properties unrelated to the sign of charge, so options B, C, and D do not apply.

A negative net charge means that the algebraic sum of negative charge is greater than the positive charge in the system. This can occur because of excess electrons, while protons may still be present in the matter. Thus the complete absence of protons is not required. Options B, C, and D express consequences or possible descriptions of a negative net charge, so option A is the statement that is not necessary.

The governing concept is net charge. A neutral body has zero algebraic charge, meaning the total positive charge balances the total negative charge. It can still contain protons, electrons, and other charged particles; neutrality does not mean that charged particles are absent. It also does not imply that the body consists only of neutrons or has zero mass. Hence option A correctly describes neutrality.

Conservation of electric charge is a fundamental principle, not a rule restricted to one charging method. In an isolated system, the algebraic sum of charge remains constant during friction, conduction, induction, electron transfer, and other electric processes. Charge may move between bodies or be redistributed, but it is not created or destroyed. Therefore option A is correct, while B, C, and D incorrectly limit the law to one process.

The governing concept is charge quantization and the sign of electronic charge. Each electron carries charge −e, so an excess of eight electrons contributes q = 8(−e) = −8e. Therefore the object has a negative charge whose magnitude is eight elementary charges, making option A correct. Option B has the wrong sign, option C has the wrong magnitude, and option D would require equal positive and negative charges.

A positive net charge means that the object has fewer electrons than positive charges, assuming ordinary charging occurs through electron transfer. Since one missing electron corresponds to +e, a charge of +4e indicates a deficiency of four electrons; equivalently, the object has lost four electrons. Thus option A is correct. Gaining electrons would produce −4e, neutrons do not determine ordinary net charge, and a charged object is not neutral.

Before contact, the two-sphere system has total charge +8 C + 0 C = +8 C. Identical conducting spheres share charge equally after touching because they reach the same potential and have the same capacitance. Thus each sphere obtains +8 C ÷ 2 = +4 C. The first sphere therefore has +4 C, so option A is correct. +8 C is the original total, +16 C violates conservation, and zero is inconsistent with the positive total.

Quantization of charge means that the net charge on an isolated body is q = ne, where n is an integer and e is the elementary charge magnitude. Thus allowed values are 0, ±e, ±2e, and so on, rather than arbitrary fractions of e. Option A states this principle exactly. Option B describes a continuous, not quantized, quantity; options C and D are unrelated and scientifically false.

The negative sign indicates an excess of negative charge. In ordinary charging processes, electrons are transferred while the heavy positive nuclei remain bound in the material. Since each added electron contributes −e, five added electrons produce q = 5(−e) = −5e. Therefore option A is correct. Losing electrons would give a positive charge, and the proton-loss statement does not describe the usual process for an ordinary object.

The governing concept is conservation of electric charge: charge cannot be created or destroyed, although it can be transferred. During friction, electrons move from one material to the other. If one object loses a quantity of electrons and becomes positive, the other gains the same quantity and becomes negative. Thus the algebraic sum of charge before and after rubbing remains unchanged. Option A is correct; B ignores the opposite signs, while C and D contradict conservation.

For an isolated system, conservation of charge requires the final algebraic total to equal the initial total. Let the unknown charge be q. Since the initial total is zero, +12 microcoulombs + q = 0. Therefore q = -12 microcoulombs. Option A is correct. A positive twelve would make the total +24, zero would leave +12, and positive twenty-four would increase the imbalance rather than cancel it.

Charge conservation states that the final total charge is +5 C. If the unknown final charge is q and one part has +2 C, then +2 C + q = +5 C. Subtracting +2 C from both sides gives q = +3 C. Thus option A is correct. A value of -3 C gives a total of -1 C, +7 C gives +9 C, and zero gives only +2 C, so those choices violate the stated total.