1. Which statement best describes electric charge in elementary electrostatics?
ⓐ. A vector quantity whose direction is represented by its sign
ⓑ. A scalar quantity that can have only positive values
ⓒ. A scalar quantity that may carry positive or negative sign
ⓓ. A vector quantity whose direction is always along the electric field
Correct Answer: A scalar quantity that may carry positive or negative sign
Explanation: Electric charge is treated as a scalar physical quantity, so it does not have a direction in space like velocity, force, or electric field. The signs \(+\) and \(-\) represent two kinds of charge, not two opposite vector directions. A charge \(+q\) and a charge \(-q\) differ in their electrical nature and in how they interact with other charges. Like charges repel and unlike charges attract because of the sign combination of the interacting charges. The vector direction appears in quantities such as electrostatic force \(\vec{F}\) and electric field \(\vec{E}\), not in charge itself. A common mistake is to treat \(+\) as “rightward” and \(-\) as “leftward,” but the sign of charge is not a spatial arrow.
2. A particle has charge \(-3.2\times10^{-19}\,\text{C}\). What is the most accurate interpretation of the negative sign?
ⓐ. The particle has no role in electrostatic interaction
ⓑ. The particle’s charge is directed opposite to its velocity
ⓒ. The particle must move toward the negative \(x\)-axis
ⓓ. The particle carries negative charge
Correct Answer: The particle carries negative charge
Explanation: The negative sign attached to charge tells the type of charge carried by the particle. It does not tell the direction of motion, the direction of force, or the direction of an axis. Charge is scalar, so \(-3.2\times10^{-19}\,\text{C}\) means a signed scalar amount of charge. The force on this charge depends on the surrounding electric field or on other charges, not on the sign alone. For example, a negative charge in a given electric field experiences force opposite to \(\vec{E}\), but that is a force-direction rule, not a charge-direction rule. A common mistake is confusing the sign of a scalar with the direction of a vector.
3. Assertion: Electric charge is a scalar quantity even though it can be positive or negative.
Reason: The signs \(+\) and \(-\) of charge specify charge type, not direction in space.
ⓐ. Both Assertion and Reason are true, and Reason explains Assertion
ⓑ. Both Assertion and Reason are true, but Reason does not explain Assertion
ⓒ. Assertion is true, but Reason is false
ⓓ. Assertion is false, but Reason is true
Correct Answer: Both Assertion and Reason are true, and Reason explains Assertion
Explanation: The Assertion is true because electric charge has magnitude and sign but no independent spatial direction. A vector requires both magnitude and direction, such as \(\vec{F}\), \(\vec{E}\), or displacement. The Reason is also true because \(+\) and \(-\) mark the two types of electric charge. These signs are used to decide whether two charges attract or repel, but they do not behave like vector arrows. The Reason directly explains why charge remains scalar despite being signed. A common mistake is to think every signed quantity is automatically a vector; signed scalars such as charge can still be non-vector quantities.
4. Complete the statement correctly: In electrostatics, like charges ______ and unlike charges ______.
ⓐ. attract; repel
ⓑ. repel; attract
ⓒ. attract; attract
ⓓ. repel; repel
Correct Answer: repel; attract
Explanation: Two charges of the same kind, such as \(+q\) and \(+Q\) or \(-q\) and \(-Q\), repel each other. Two charges of opposite kind, such as \(+q\) and \(-Q\), attract each other. This attraction or repulsion is a basic observed property of electric charge. The rule depends on the signs of both interacting charges, not on the absolute size of one charge alone. The actual magnitude of force needs Coulomb’s law, but the attractive or repulsive nature is decided by the sign combination. A useful check is that same signs push apart, while opposite signs pull together.
5. Study the table and identify the row with the incorrect description.
| Row | Quantity or symbol | Description |
|---|
| P | Electric charge | Scalar quantity with sign |
| Q | \(+\) and \(-\) | Two kinds of charge |
| R | \(\text{C}\) | SI unit of electric charge |
| S | Sign of charge | Direction of charge as a vector |
ⓐ. Row P
ⓑ. Row Q
ⓒ. Row R
ⓓ. Row S
Correct Answer: Row S
Explanation: Row P is correct because electric charge is a scalar quantity but it is written with a sign. Row Q is correct because positive and negative are the two kinds of electric charge. Row R is correct because the SI unit of electric charge is the coulomb, written as \(\text{C}\). Row S is incorrect because the sign of charge is not a vector direction. The sign affects attraction, repulsion, and the direction of force in a field, but it does not give charge itself a spatial direction. The most common confusion is mixing up signed scalar charge with vector quantities such as \(\vec{F}\) and \(\vec{E}\).
6. The SI unit of electric charge is \(\text{C}\). Using the relation \(q=It\), what is the dimensional formula of charge?
ⓐ. \([A T]\)
ⓑ. \([A T^{-1}]\)
ⓒ. \([M L T^{-2}]\)
ⓓ. \([M L^2 T^{-2} A^{-1}]\)
Correct Answer: \([A T]\)
Explanation: \( \textbf{Given relation:} \) Electric charge is related to current and time by \(q=It\).
\( \textbf{Dimensional meaning:} \) Current has dimension \([A]\), where \(\text{A}\) is ampere.
\( \textbf{Time dimension:} \) Time has dimension \([T]\).
\( \textbf{Applying the relation:} \)
\[
[q]=[I][t]
\]
\( \textbf{Substitution of dimensions:} \)
\[
[q]=[A][T]
\]
\( \textbf{Simplified dimensional formula:} \)
\[
[q]=[A T]
\]
\( \textbf{Unit check:} \) Since \(1\,\text{C}=1\,\text{A}\,\text{s}\), the dimension \([A T]\) is consistent.
\( \textbf{Final answer:} \) The dimensional formula of charge is \([A T]\).
7. Which pair correctly matches the quantity with its usual symbol or unit?
| Column I | Column II |
|---|
| P. Electric charge | 1. \(\text{C}\) |
| Q. Elementary charge | 2. \(e\) |
| R. Dimension of charge | 3. \([A T]\) |
| S. Force | 4. \(\text{N}\) |
ⓐ. P-1, Q-2, R-3, S-4
ⓑ. P-2, Q-1, R-3, S-4
ⓒ. P-1, Q-3, R-2, S-4
ⓓ. P-4, Q-2, R-3, S-1
Correct Answer: P-1, Q-2, R-3, S-4
Explanation: Electric charge is measured in coulomb, so \(P\) matches \(1\). Elementary charge is represented by \(e\), so \(Q\) matches \(2\). The dimensional formula of charge is \([A T]\), so \(R\) matches \(3\). Force is measured in newton, so \(S\) matches \(4\). This matching also separates the scalar charge quantity from the vector force quantity. A useful notation check is that \(\text{C}\) is a unit, \(e\) is a symbol for a fundamental charge magnitude, and \([A T]\) is a dimensional formula.
8. Two small bodies carry charges \(+2\,\text{C}\) and \(-5\,\text{C}\). Which statement correctly describes the nature of their electrostatic interaction?
ⓐ. They repel because the magnitudes \(2\) and \(5\) are unequal
ⓑ. They attract because their charges have opposite signs
ⓒ. They do not interact because the total charge is negative
ⓓ. They repel because one charge is larger in magnitude
Correct Answer: They attract because their charges have opposite signs
Explanation: The nature of electrostatic interaction is decided first by the relative signs of the two charges. A positive charge and a negative charge form an unlike pair, so they attract each other. The unequal magnitudes \(2\,\text{C}\) and \(5\,\text{C}\) affect the magnitude of the force, not whether the interaction is attractive or repulsive. The total charge of the two-body system, \(+2\,\text{C}+(-5\,\text{C})=-3\,\text{C}\), does not decide whether the two bodies attract each other. Attraction or repulsion is a pairwise sign rule. A common mistake is to use net charge or larger magnitude to decide the force nature, but the sign combination is the deciding factor here.
9. Read the situation below and answer the question.
A student writes, “A charge of \(-q\) is directed downward because the negative sign shows direction.” Another student says, “The charge is negative, but the direction of force must be decided from the interaction or field.”
Which conclusion is correct?
ⓐ. The first student is correct because negative quantities are always downward vectors
ⓑ. The first student is correct only if \(q\) is measured in \(\text{C}\)
ⓒ. The second student is correct because charge sign is not itself a spatial direction
ⓓ. Both students are wrong because negative charge cannot exert or experience force
Correct Answer: The second student is correct because charge sign is not itself a spatial direction
Explanation: A negative charge is a scalar quantity with a negative sign; it is not automatically directed downward, leftward, or backward. Direction belongs to vector quantities such as force and electric field. The force on a charge depends on the arrangement of other charges or on the direction of the electric field. For example, the same \(-q\) can experience upward, downward, leftward, or rightward force depending on the physical situation. The unit \(\text{C}\) tells that the quantity is charge, but it does not create a vector direction. A useful habit is to separate “sign of charge” from “direction of force.”
10. Consider the following statements about electric charge.
Statement I: Electric charge has SI unit \(\text{C}\).
Statement II: Electric charge is a scalar quantity with positive or negative sign.
Statement III: The signs \(+\) and \(-\) of charge represent opposite directions along a chosen axis.
Statement IV: Electric charge plays a role in electrostatic attraction and repulsion.
Which statements are correct?
ⓐ. II, III and IV only
ⓑ. I, II, III and IV
ⓒ. I and III only
ⓓ. I, II and IV only
Correct Answer: I, II and IV only
Explanation: Statement I is correct because the SI unit of electric charge is the coulomb, written as \(\text{C}\). Statement II is also correct because charge is scalar but signed. Statement III is incorrect because \(+\) and \(-\) do not represent opposite spatial directions; they represent two kinds of charge. Statement IV is correct because electrostatic interactions arise because bodies possess electric charge. The signs of charges decide whether the interaction is attraction or repulsion, while Coulomb’s law later decides the force magnitude. The key distinction is that charge affects vector forces, but charge itself is not a vector.
11. Use the arrangement described below.
Two identical light pith balls are suspended by insulating threads. Ball P is given charge \(+q\), and ball Q is also given charge \(+q\). The balls are brought near each other without touching.
What is the expected electrostatic behaviour?
ⓐ. They attract because both have equal magnitudes
ⓑ. They repel because both charges are positive
ⓒ. They remain unaffected because charge is scalar
ⓓ. They attract first and then repel after contact
Correct Answer: They repel because both charges are positive
Explanation: Both pith balls carry positive charge, so they form a like-charge pair. Like charges repel, regardless of whether the charges are placed on light pith balls, metal spheres, or other bodies. The fact that charge is scalar does not mean it has no physical effect; it means charge has no vector direction of its own. The electrostatic force produced by charge is a vector and can push the balls apart. Equal magnitude is not the reason for repulsion; same sign is the reason. The clean rule is: same kind of charge gives repulsion, opposite kind gives attraction.
12. Which option correctly compares charge and electrostatic force?
ⓐ. Charge is vector and electrostatic force is scalar
ⓑ. Both charge and electrostatic force are scalars
ⓒ. Charge is scalar, while electrostatic force is vector
ⓓ. Both charge and electrostatic force are vectors because both can be positive or negative
Correct Answer: Charge is scalar, while electrostatic force is vector
Explanation: Electric charge is a scalar physical quantity with sign. It does not require a direction in space for its complete description. Electrostatic force, however, has both magnitude and direction, so it is a vector quantity. The direction of electrostatic force depends on the positions of charges and whether the interaction is attractive or repulsive. A positive or negative sign on charge is not enough to make charge a vector. The important comparison is that charge is the property responsible for interaction, while force is the directed interaction produced because of charges.
13. Why do metals behave as good conductors in electrostatics?
ⓐ. Their positive ions move freely throughout the metal
ⓑ. Their electrons are free to move through the body
ⓒ. Their atoms do not contain any bound charges
ⓓ. Their net charge must always be zero
Correct Answer: Their electrons are free to move through the body
Explanation: Metals contain many electrons that are not tightly bound to individual atoms. These mobile electrons can move through the body of the conductor when an electric influence is applied. The positive ions in a metal are fixed in the lattice and do not move freely through the solid as charge carriers in ordinary electrostatics. A conductor can have zero net charge or non-zero net charge, so neutrality is not the reason for conductivity. The important feature is mobility of charge, especially electrons in metals. The common mistake is to think positive charge physically flows through a metal in the same way as electrons; in metallic conductors, the mobile charge carriers are electrons.
14. Which statement best distinguishes a conductor from an insulator?
ⓐ. A conductor allows charge redistribution, while an insulator restricts it
ⓑ. A conductor can have electric charge, while an insulator can never have electric charge
ⓒ. A conductor always has positive charge, while an insulator always has negative charge
ⓓ. A conductor attracts charges, while an insulator repels all charges
Correct Answer: A conductor allows charge redistribution, while an insulator restricts it
Explanation: A conductor contains mobile charges that can move through the material. Because of this mobility, excess charge or induced charge can redistribute over the conductor. An insulator can also be charged, but its charges are not free to move through the entire body. Charge placed on an insulator often remains localised near the region where it is placed. The distinction is not about whether a material can be charged, but about how freely charge can move inside it. A useful check is that “conducting” means charge mobility, not automatic positive charge or automatic attraction.
15. A charged plastic rod touches one small region of an insulating rubber sheet. After contact, the excess charge remains mainly near the touched region. Which property of the rubber sheet explains this observation?
ⓐ. It has no atoms that can hold charge
ⓑ. It allows positive ions to move freely
ⓒ. It restricts charge movement through its body
ⓓ. It converts electric charge into heat immediately
Correct Answer: It restricts charge movement through its body
Explanation: Rubber is an insulator, so charges placed on it are not free to move through the whole material. When a charged body touches one region of an insulator, the transferred charge tends to stay close to the region of contact. This is different from a conductor, where mobile electrons can redistribute over the surface. The charge does not vanish simply because the material is insulating. It also does not spread uniformly unless charge mobility or an external process allows redistribution. A common mistake is to think “insulator” means “cannot be charged”; it actually means charges are not free to move easily through it.
16. Assertion: Excess charge given to a metal sphere can spread over its surface.
Reason: A metal has mobile electrons that can redistribute under electrostatic forces.
ⓐ. Both Assertion and Reason are true, and Reason explains Assertion
ⓑ. Both Assertion and Reason are true, but Reason does not explain Assertion
ⓒ. Assertion is true, but Reason is false
ⓓ. Assertion is false, but Reason is true
Correct Answer: Both Assertion and Reason are true, and Reason explains Assertion
Explanation: The Assertion is true because a metal sphere is a conductor, so excess charge does not remain confined to the exact point of contact. The Reason is also true because metals contain mobile electrons that can move through the conductor. When charge is supplied, electrostatic repulsion and attraction make these mobile charges rearrange. This redistribution continues until electrostatic equilibrium is reached. The Reason explains the physical cause behind the spreading of excess charge. The key contrast is that the same behaviour would not occur so freely on an insulating body.
17. A neutral metal sphere is placed near a positively charged rod without touching it. What happens inside the sphere?
ⓐ. Electrons shift slightly toward the rod, causing charge redistribution
ⓑ. Protons move toward the rod and leave the metal lattice
ⓒ. The sphere becomes permanently positively charged without any charge exchange
ⓓ. All charges inside the sphere disappear
Correct Answer: Electrons shift slightly toward the rod, causing charge redistribution
Explanation: A positively charged rod attracts the mobile electrons in the neutral metal sphere. These electrons shift slightly toward the side nearer the rod, leaving the far side relatively positive. The total charge of the isolated sphere remains zero because no charge has entered or left it. The positive ions of the metal do not leave their lattice positions in ordinary electrostatic induction. This process is charge redistribution, not creation or destruction of charge. The important distinction is that a conductor can show separated positive and negative regions while still having zero net charge.
18. Study the table and identify the row with the correct material behaviour.
| Row | Material type | Charge behaviour |
|---|
| P | Conductor | Excess charge can redistribute through mobile charges |
| Q | Insulator | Excess charge always spreads instantly over the whole body |
| R | Metal | Conduction occurs mainly by free proton motion |
| S | Insulator | It cannot contain electric charge |
ⓐ. Row Q
ⓑ. Row R
ⓒ. Row S
ⓓ. Row P
Correct Answer: Row P
Explanation: Row P correctly describes a conductor because mobile charges can redistribute through it. Row Q is wrong because an insulator does not allow excess charge to spread freely through the whole body. Row R is wrong because metallic conduction is mainly due to mobile electrons, not free proton motion. Row S is wrong because an insulator can contain charge; it simply does not allow charge to move freely. The table is testing charge mobility, not the ability of a material to possess charge. The most common confusion is equating insulation with absence of charge, but insulation means restricted charge motion.
19. A conducting sphere and an insulating sphere are both touched at one point by the same negatively charged rod. Which comparison is most reasonable immediately after charging?
ⓐ. Conductor redistributes electrons; insulator keeps them near contact
ⓑ. The insulator redistributes excess electrons faster because its charges are bound
ⓒ. Both bodies must spread charge uniformly through their volumes
ⓓ. Neither body can receive charge because both were neutral initially
Correct Answer: Conductor redistributes electrons; insulator keeps them near contact
Explanation: When a negatively charged rod touches a conductor, electrons can move because the conductor has mobile charge carriers. The excess charge can therefore redistribute, especially over the surface of the conductor. In an insulator, transferred charge is much less free to move, so it remains more localised near the contact region. Neutrality before contact does not prevent charge transfer; it only means the initial net charge was zero. The difference comes from charge mobility inside the material. A good physical picture is that conductors allow charge rearrangement, while insulators resist large-scale charge movement.
20. Complete the statement correctly: Grounding a charged conductor means connecting it to Earth so that ______.
ⓐ. protons are removed from all atoms of the conductor
ⓑ. the conductor becomes an insulator
ⓒ. the total charge of the universe becomes zero
ⓓ. charge can flow between the conductor and Earth
Correct Answer: charge can flow between the conductor and Earth
Explanation: Grounding means connecting a conductor to Earth through a conducting path. Earth is a very large reservoir of charge, so electrons may flow between the object and Earth depending on the electrical condition. A negatively charged conductor may lose excess electrons to Earth, while a positively charged conductor may receive electrons from Earth. Grounding does not change a conductor into an insulator. It also does not destroy charge; it permits charge transfer between the object and Earth. The useful reminder is that grounding is a charge-exchange process, not a charge-creation process.
