1. Which statement best describes electric charge as a physical quantity?
ⓐ. Electric charge is a vector quantity directed along the force.
ⓑ. Electric charge is a vector quantity directed along the electric field.
ⓒ. Electric charge is a scalar quantity that can only be positive.
ⓓ. Electric charge is a scalar quantity that may be positive or negative.
Correct Answer: Electric charge is a scalar quantity that may be positive or negative.
Explanation: Electric charge is a basic property of matter responsible for electrostatic interaction. It is treated as a scalar physical quantity because it does not have a direction in space like displacement, velocity, or force. The signs \(+\) and \(-\) attached to charge are not spatial directions; they indicate two different kinds of charge. A positive charge and a negative charge interact differently, but the charge itself is still not a vector. The quantity is commonly represented by the symbol \(q\). Its SI unit is the coulomb, written as \(\text{C}\). Therefore, a charge such as \(+3\,\text{C}\) or \(-3\,\text{C}\) has sign and magnitude, but no vector direction.
2. Two small charged bodies are brought near each other. In which case will the electrostatic force between them be attractive?
ⓐ. Both bodies have charges \(+q\) and \(+2q\)
ⓑ. Both bodies have charges \(+2q\) and \(+3q\)
ⓒ. Both bodies have charges \(-q\) and \(-2q\)
ⓓ. Charges \(+q\) and \(-2q\)
Correct Answer: Charges \(+q\) and \(-2q\)
Explanation: Electrostatic interaction depends on the signs of the two charges. Like charges repel each other, so two positive charges repel and two negative charges also repel. Unlike charges attract each other, so a positive charge and a negative charge pull toward each other. The magnitudes \(q\), \(2q\), or \(3q\) affect the strength of the force, but the attractive or repulsive nature is decided by the signs. A pair such as \(+q\) and \(-2q\) has opposite signs. Hence, the force between these two charged bodies is attractive.
3. A body has charge \(q=-4\,\mu\text{C}\). Which interpretation of the negative sign is physically meaningful?
ⓐ. The charge has a direction opposite to motion.
ⓑ. The charge has a direction opposite to force.
ⓒ. The body has no electrostatic interaction.
ⓓ. The body carries negative charge.
Correct Answer: The body carries negative charge.
Explanation: The negative sign in \(q=-4\,\mu\text{C}\) tells the kind of charge carried by the body. It does not mean that charge points in a direction, because electric charge is a scalar quantity. Direction is meaningful for vector quantities such as \(\vec{F}\) or \(\vec{E}\), not for \(q\) itself. A negative charge can still experience force when placed near another charge or in an electric field. The sign helps decide whether the interaction with another charge is attraction or repulsion. Thus, \(-4\,\mu\text{C}\) means a negative charge of magnitude \(4\,\mu\text{C}\).
4. Which option correctly gives the usual symbol, SI unit, and dimensional formula of electric charge?
ⓐ. Symbol \(I\), unit \(\text{A}\), dimension \([A]\)
ⓑ. Symbol \(q\), unit \(\text{C}\), dimension \([AT]\)
ⓒ. Symbol \(V\), unit \(\text{J C}^{-1}\), dimension \([ML^2T^{-3}A^{-1}]\)
ⓓ. Symbol \(F\), unit \(\text{N}\), dimension \([MLT^{-2}]\)
Correct Answer: Symbol \(q\), unit \(\text{C}\), dimension \([AT]\)
Explanation: \( \textbf{Known idea:} \) Electric charge is commonly represented by \(q\).
\( \textbf{SI unit:} \) The SI unit of charge is coulomb, written as \(\text{C}\).
\( \textbf{Dimensional relation:} \) Charge is related to current and time by \(q=It\).
\( \textbf{Dimension of current:} \) Electric current has dimension \([A]\).
\( \textbf{Dimension of time:} \) Time has dimension \([T]\).
\( \textbf{Combining dimensions:} \) Therefore, \([q]=[I][t]=[A][T]=[AT]\).
\( \textbf{Result:} \) The correct combination is symbol \(q\), unit \(\text{C}\), and dimension \([AT]\).
5. Which statement correctly compares the sign of electric charge with the direction of a vector?
ⓐ. The sign of charge gives the direction in which the charged body must move.
ⓑ. The sign of charge gives the direction of the electric field produced by the charge.
ⓒ. The sign of charge converts electric charge into a vector quantity.
ⓓ. The sign distinguishes charge type, not spatial direction.
Correct Answer: The sign distinguishes charge type, not spatial direction.
Explanation: Electric charge has a sign, but sign and direction are not the same idea. A vector needs both magnitude and direction in space, such as east, west, upward, or along a chosen axis. Charge does not point in any spatial direction. The signs \(+\) and \(-\) are used to distinguish two types of charge. These signs decide whether two charges attract or repel. For example, \(+q\) and \(-q\) are unlike charges, while \(+q\) and \(+2q\) are like charges. Therefore, electric charge remains a scalar quantity even though it may be positive or negative.
6. Two objects carry charges \(+5\,\text{nC}\) and \(+1\,\text{nC}\). What can be concluded about the nature of their electrostatic interaction?
ⓐ. They attract because their magnitudes are unequal.
ⓑ. They do not interact because both are positive.
ⓒ. They attract because one charge is smaller.
ⓓ. They repel because the signs are the same.
Correct Answer: They repel because the signs are the same.
Explanation: The nature of electrostatic interaction is decided by the signs of the charges. Both charges here are positive, so they are like charges. Like charges repel each other even if their magnitudes are different. The values \(5\,\text{nC}\) and \(1\,\text{nC}\) would influence the force magnitude, not change repulsion into attraction. Unequal magnitudes do not make like charges attractive. A positive charge still interacts with another positive charge. Hence, these two objects repel each other.
7. Which pair shows like charges?
ⓐ. \(+3\,\text{C}\) and \(-3\,\text{C}\)
ⓑ. \(+2\,\text{C}\) and \(-5\,\text{C}\)
ⓒ. \(-4\,\text{C}\) and \(-1\,\text{C}\)
ⓓ. \(+1\,\text{C}\) and \(-1\,\text{C}\)
Correct Answer: \(-4\,\text{C}\) and \(-1\,\text{C}\)
Explanation: Like charges are charges of the same kind. A positive-positive pair is a like-charge pair, and a negative-negative pair is also a like-charge pair. The numerical magnitudes do not have to be equal for the charges to be like charges. In the pair \(-4\,\text{C}\) and \(-1\,\text{C}\), both charges are negative. Since both signs are the same, the charges are like charges. Such a pair would repel if placed near each other.
8. A student says, “A charge of \(-2\,\text{C}\) is smaller than a charge of \(+1\,\text{C}\), so it must produce a weaker electrostatic interaction in every comparison.” What is the main error in this statement?
ⓐ. The sign of charge is being confused with vector direction.
ⓑ. The unit \(\text{C}\) is being confused with current.
ⓒ. The charge symbol \(q\) is being confused with mass.
ⓓ. It treats signed value as magnitude.
Correct Answer: It treats signed value as magnitude.
Explanation: A charge such as \(-2\,\text{C}\) has negative type and magnitude \(2\,\text{C}\). A charge such as \(+1\,\text{C}\) has positive type and magnitude \(1\,\text{C}\). The negative sign does not make the amount of charge smaller in the sense of magnitude. For strength-related comparisons, the magnitude \(|q|\) is the relevant amount of charge. The sign decides the type of interaction with another charge, such as attraction or repulsion. Therefore, \(-2\,\text{C}\) has a greater magnitude of charge than \(+1\,\text{C}\), even though its signed numerical value is negative.
9. Which statement is consistent with the conventional naming of the two kinds of electric charge?
ⓐ. The two kinds are called fast and slow charges.
ⓑ. The two kinds are called north and south charges.
ⓒ. The two kinds are called heavy and light charges.
ⓓ. They are called positive and negative charges.
Correct Answer: They are called positive and negative charges.
Explanation: Electric charge exists in two kinds, conventionally named positive charge and negative charge. These names are conventions, but they are used consistently in electrostatics. The words positive and negative do not mean physically better or worse; they label two opposite kinds of charge. Like kinds repel, so positive repels positive and negative repels negative. Unlike kinds attract, so positive attracts negative. Terms such as north and south are used for magnetic poles, not electric charges. Therefore, the standard names are positive charge and negative charge.
10. The dimensional formula of electric charge is \([AT]\). Which reasoning supports this result?
ⓐ. Since \(q=\frac{I}{t}\), \([q]=[AT^{-1}]\)
ⓑ. Since \(q=It\), \([q]=[AT]\)
ⓒ. Since \(q=\frac{t}{I}\), \([q]=[A^{-1}T]\)
ⓓ. Since \(q=I^2t\), \([q]=[A^2T]\)
Correct Answer: Since \(q=It\), \([q]=[AT]\)
Explanation: \( \textbf{Starting relation:} \) Electric current is rate of flow of charge, so \(I=\frac{q}{t}\).
\( \textbf{Rearranging:} \) Multiplying both sides by \(t\), we get \(q=It\).
\( \textbf{Dimension of current:} \) The dimension of current is \([A]\).
\( \textbf{Dimension of time:} \) The dimension of time is \([T]\).
\( \textbf{Dimensional substitution:} \) \([q]=[I][t]=[A][T]\).
\( \textbf{Final result:} \) Thus, electric charge has dimensional formula \([AT]\), matching the unit coulomb \(\text{C}\).
11. Which of the following is a correct statement about electrostatic interaction?
ⓐ. It occurs only between bodies carrying equal amounts of charge.
ⓑ. It occurs only when one body is positive and the other is negative.
ⓒ. It is possible only when the charged bodies are moving.
ⓓ. It is linked to the presence of electric charge.
Correct Answer: It is linked to the presence of electric charge.
Explanation: Electrostatic interaction arises because bodies possess electric charge. It can be attractive or repulsive depending on the signs of the charges. Opposite signs produce attraction, while same signs produce repulsion. The charges do not have to be equal in magnitude for an interaction to occur. The bodies also need not be moving, because electrostatics deals with charges at rest. The presence and nature of charge are the essential conditions for electrostatic interaction. Therefore, electric charge is the property responsible for such interaction.
12. Four descriptions of a charged body are given. Which one is physically complete and correctly worded?
ⓐ. The body has charge \(3\) in the direction of \(+\text{C}\).
ⓑ. The body has charge \(3\,\text{C}\) but no sign is needed.
ⓒ. The body has charge \(+3\,\text{C}\), where \(+\) gives vector direction.
ⓓ. The body has charge \(+3\,\text{C}\), where \(+\) gives charge type.
Correct Answer: The body has charge \(+3\,\text{C}\), where \(+\) gives charge type.
Explanation: A proper charge description should include magnitude, sign, and unit whenever needed. In \(+3\,\text{C}\), the magnitude is \(3\,\text{C}\). The sign \(+\) tells that the body carries positive charge. The sign is not a vector direction, so it should not be interpreted as a direction in space. The unit \(\text{C}\) is necessary because charge is measured in coulomb in the SI system. Saying only \(3\) is incomplete because the unit is missing. Thus, \(+3\,\text{C}\) correctly describes a positive charge of magnitude \(3\,\text{C}\).
13. A particle is described as having charge \(-8\,\text{nC}\). Which statement about this charge is most accurate?
ⓐ. Its magnitude is \(-8\,\text{nC}\), and its type is neutral.
ⓑ. Its magnitude is \(8\,\text{nC}\), and its type is negative.
ⓒ. Its magnitude is \(8\,\text{C}\), and its type is negative.
ⓓ. Its magnitude is \(-8\,\text{C}\), and its type is positive.
Correct Answer: Its magnitude is \(8\,\text{nC}\), and its type is negative.
Explanation: The sign of charge tells the type of charge, while the magnitude tells the amount of charge. For \(q=-8\,\text{nC}\), the negative sign indicates negative charge. The magnitude is written as \(|q|=8\,\text{nC}\). A magnitude is never negative, because magnitude represents size only. The unit \(\text{nC}\) means nanocoulomb, not coulomb directly. Therefore, the charge has negative type and amount \(8\,\text{nC}\).
14. A body carries charge \(+0.004\,\text{C}\). Which option represents the same charge in \(\mu\text{C}\)?
ⓐ. \(4.0\times10^2\,\mu\text{C}\)
ⓑ. \(4.0\times10^3\,\mu\text{C}\)
ⓒ. \(4.0\times10^4\,\mu\text{C}\)
ⓓ. \(4.0\times10^5\,\mu\text{C}\)
Correct Answer: \(4.0\times10^3\,\mu\text{C}\)
Explanation: \( \textbf{Given charge:} \) \(q=+0.004\,\text{C}\).
\( \textbf{Required unit:} \) Convert the charge into \(\mu\text{C}\).
\( \textbf{Unit relation:} \) \(1\,\mu\text{C}=10^{-6}\,\text{C}\), so \(1\,\text{C}=10^6\,\mu\text{C}\).
\( \textbf{Conversion step:} \) \(0.004\,\text{C}=0.004\times10^6\,\mu\text{C}\).
\( \textbf{Simplification:} \) \(0.004=4.0\times10^{-3}\), so \(0.004\times10^6=4.0\times10^3\).
\( \textbf{Sign check:} \) The charge remains positive because unit conversion does not change the kind of charge.
\( \textbf{Final result:} \) \(q=+4.0\times10^3\,\mu\text{C}\).
15. Which observation directly shows that charge is responsible for electrostatic interaction?
ⓐ. A neutral plastic scale bends when pressed by hand.
ⓑ. A stone slows down while moving on rough ground.
ⓒ. A metal ball falls downward when released.
ⓓ. A rubbed comb attracts small dry paper bits.
Correct Answer: A rubbed comb attracts small dry paper bits.
Explanation: Electrostatic interaction is associated with the presence of electric charge. When a comb is rubbed, it can become charged due to transfer of electrons. The charged comb can then attract small pieces of dry paper through electric interaction. This attraction is different from ordinary mechanical pushing, gravitational falling, or frictional slowing. The paper bits may initially be neutral, but charges within them can redistribute slightly in response to the charged comb. That redistribution allows an attractive electrostatic effect to occur. Hence, a rubbed comb attracting dry paper bits is a familiar sign of electrostatic interaction.
16. During rubbing, a glass rod loses some electrons to a silk cloth. What are the final charges on the rod and cloth?
ⓐ. The rod becomes negative, and the cloth becomes positive.
ⓑ. Both the rod and the cloth become negative.
ⓒ. Both the rod and the cloth become positive.
ⓓ. The rod becomes positive, and the cloth becomes negative.
Correct Answer: The rod becomes positive, and the cloth becomes negative.
Explanation: Electrons carry negative charge. If a body loses electrons, it loses some negative charge. After losing negative charge, the body is left with an excess of positive charge and becomes positively charged. In this case, the glass rod loses electrons, so the glass rod becomes positive. The silk cloth gains those electrons, so it gains negative charge. Rubbing does not create opposite charges from nothing; it transfers electrons from one body to the other. Thus, the rod becomes positive and the cloth becomes negative.
17. A plastic rod is rubbed with fur and becomes negatively charged. What must have happened during rubbing?
ⓐ. The rod lost protons to the fur.
ⓑ. The rod lost electrons to the fur.
ⓒ. The rod gained protons from the fur.
ⓓ. The rod gained electrons.
Correct Answer: The rod gained electrons.
Explanation: A body becomes negatively charged when it gains excess electrons. Protons are bound inside atomic nuclei and are not transferred in ordinary rubbing processes. The mobile charge transfer in such electrostatic charging usually involves electrons. Since the plastic rod becomes negative, it must have received electrons from the fur. The fur, after losing electrons, is left relatively positive. The total charge of the rod-fur pair remains conserved if the pair is treated as an isolated system. Therefore, the negative charge of the rod is due to gain of electrons.
18. Two initially neutral insulating bodies are rubbed together. After rubbing, body \(X\) has charge \(+6\,\text{nC}\). If no charge escapes to the surroundings, what is the charge on body \(Y\)?
ⓐ. \(+6\,\text{nC}\)
ⓑ. \(-3\,\text{nC}\)
ⓒ. \(-6\,\text{nC}\)
ⓓ. \(+3\,\text{nC}\)
Correct Answer: \(-6\,\text{nC}\)
Explanation: \( \textbf{Initial state:} \) Both bodies are initially neutral, so the total initial charge is \(0\,\text{nC}\).
\( \textbf{After rubbing:} \) Body \(X\) has charge \(+6\,\text{nC}\).
\( \textbf{Key principle:} \) Rubbing transfers charge between bodies; it does not create net charge in the isolated pair.
\( \textbf{Charge balance:} \) The final total charge must remain \(0\,\text{nC}\).
\( \textbf{Equation:} \) \(q_X+q_Y=0\).
\( \textbf{Substitution:} \) \(+6\,\text{nC}+q_Y=0\).
\( \textbf{Solving:} \) \(q_Y=-6\,\text{nC}\).
\( \textbf{Final result:} \) Body \(Y\) must have charge \(-6\,\text{nC}\).
19. Which statement best explains why rubbing two suitable materials can charge them?
ⓐ. Rubbing creates new electrons on one material.
ⓑ. Rubbing destroys protons from one material.
ⓒ. Rubbing converts mass directly into charge.
ⓓ. Rubbing separates charge by electron transfer.
Correct Answer: Rubbing separates charge by electron transfer.
Explanation: In ordinary frictional charging, electrons are transferred from one material to another. The material that loses electrons becomes positively charged. The material that gains electrons becomes negatively charged. The process is a separation of charge, not a creation of net charge from nothing. Protons are not normally transferred because they are held inside nuclei. The direction of electron transfer depends on the nature of the two materials. Therefore, rubbing can produce charged bodies because it shifts electrons between them.
20. A neutral rod and a neutral cloth are rubbed together. The rod gains a charge of \(-12\,\mu\text{C}\). Which statement is consistent with charge conservation?
ⓐ. The cloth gains \(+12\,\mu\text{C}\), so the pair remains neutral overall.
ⓑ. The cloth gains \(-12\,\mu\text{C}\), so the pair has total charge \(-24\,\mu\text{C}\).
ⓒ. The cloth remains neutral, so only the rod is charged after rubbing.
ⓓ. The cloth gains \(+6\,\mu\text{C}\), so half the charge is conserved.
Correct Answer: The cloth gains \(+12\,\mu\text{C}\), so the pair remains neutral overall.
Explanation: \( \textbf{Initial total charge:} \) The rod and cloth are both neutral at first, so \(Q_{\text{initial}}=0\).
\( \textbf{Charge on rod after rubbing:} \) \(q_{\text{rod}}=-12\,\mu\text{C}\).
\( \textbf{Conservation idea:} \) If no charge escapes, the total charge of the two-body system must stay \(0\).
\( \textbf{Final charge relation:} \) \(q_{\text{rod}}+q_{\text{cloth}}=0\).
\( \textbf{Substitution:} \) \(-12\,\mu\text{C}+q_{\text{cloth}}=0\).
\( \textbf{Solving:} \) \(q_{\text{cloth}}=+12\,\mu\text{C}\).
\( \textbf{Meaning of signs:} \) The rod gained excess electrons, while the cloth lost electrons.
\( \textbf{Final result:} \) The cloth must have \(+12\,\mu\text{C}\).
