1. The central idea of electrostatic potential is best described as:
ⓐ. A material property that exists only inside capacitors
ⓑ. A flow of charge through a conductor per second
ⓒ. A force per unit charge that always has a direction
ⓓ. A work-related scalar quantity in an electric field
Correct Answer: A work-related scalar quantity in an electric field
Explanation: Electrostatic potential is linked with the work involved in placing or moving charge in an electric field. Unlike electric field \(\vec{E}\), potential \(V\) is a scalar quantity, so it has magnitude and sign but no direction. It helps describe the energy condition of a point in an electric field without drawing a force arrow at that point. A force per unit charge describes electric field, not potential. Capacitance is a related electrostatic idea, but it means charge-storing ability rather than potential itself. The useful starting distinction is that \(\vec{E}\) describes force effect, while \(V\) describes work or energy effect per unit charge.
2. A value \(V=-20\,\text{V}\) is written for a point near a charged body. What does the negative sign show?
ⓐ. The electric field at that point must be zero
ⓑ. The potential is a vector directed toward the charged body
ⓒ. The potential is below the chosen zero level
ⓓ. The potential has a direction opposite to the electric field
Correct Answer: The potential is below the chosen zero level
Explanation: Electrostatic potential \(V\) is a scalar quantity, so a negative sign does not give a spatial direction. The sign tells whether the potential is above or below the chosen reference level. A point can have negative potential and still have a non-zero electric field \(\vec{E}\). Direction belongs to vector quantities such as \(\vec{E}\) and \(\vec{F}\), not to scalar potential. Saying \(V=-20\,\text{V}\) means the point is at a potential \(20\,\text{V}\) lower than the reference level. The sign of \(V\) should be read as an algebraic sign, not as an arrow.
3. Potential difference between two points is most directly connected with:
ⓐ. Work done per unit charge between two points
ⓑ. Surface area of a charged conductor per unit charge
ⓒ. Charge stored per unit potential difference by a conductor pair
ⓓ. Force acting per unit positive test charge at one point only
Correct Answer: Work done per unit charge between two points
Explanation: Potential difference describes how much work is associated with moving unit charge from one point to another. It compares two points, so it is not only a property of a single point. Electric field \(\vec{E}\) is related to force per unit charge, but potential difference is related to work per unit charge. Capacitance \(C\) uses potential difference in its definition, but it is not the meaning of potential difference itself. The phrase “per unit charge” is essential because the same path condition may involve different total work for different charges. Potential difference tells the work scale between two points before the actual charge value is multiplied in.
4. In a basic circuit idea, a capacitor is mainly introduced as a device that:
ⓐ. Produces charge continuously from empty space
ⓑ. Stores equal kinds of charge on both plates
ⓒ. Stores charge across a potential difference
ⓓ. Converts electric field into magnetic field permanently
Correct Answer: Stores charge across a potential difference
Explanation: A capacitor consists of two conductors separated by an insulating region. When charged, the two conductors usually carry equal and opposite charges, and a potential difference exists between them. Its usefulness comes from charge storage and energy storage, not from producing charge from nothing. The insulating gap prevents direct conduction across the plates under normal conditions. Capacitance \(C\) measures how much charge can be stored per unit potential difference. The idea of capacitance is therefore tied to \(Q\) and \(V\), not to charge creation.
5. A charged metal dome gives a spark when the electric field in nearby air becomes very large. As a broad electrostatic example, this situation mainly connects:
ⓐ. Resistance, current flow, and steady heating
ⓑ. Potential, field, and stored charge
ⓒ. Magnetic field, induction, and pole strength
ⓓ. Thermal pressure, expansion, and wave speed
Correct Answer: Potential, field, and stored charge
Explanation: A charged conductor can reach a high potential relative to its surroundings. A large potential difference over a small distance can produce a strong electric field in air. If the field becomes large enough, air may break down and a spark may occur. This example is only a broad orientation here, not a detailed study of discharge physics. It connects naturally with potential, electric field, and stored charge on conductors. The example does not depend on magnetic poles or nuclear effects.
6. Match each quantity with its basic physical idea.
| Column I | Column II |
|---|
| P. Electric field \(\vec{E}\) | 1. Charge-storing ability per unit potential difference |
| Q. Electrostatic potential \(V\) | 2. Force effect per unit positive test charge |
| R. Capacitance \(C\) | 3. Work or energy idea per unit charge |
| S. Work \(W\) | 4. Energy transferred by a force during displacement |
ⓐ. P-2, Q-3, R-1, S-4
ⓑ. P-2, Q-1, R-3, S-4
ⓒ. P-3, Q-2, R-1, S-4
ⓓ. P-4, Q-3, R-2, S-1
Correct Answer: P-2, Q-3, R-1, S-4
Explanation: Electric field \(\vec{E}\) describes the force effect per unit positive test charge. Electrostatic potential \(V\) is linked with work or energy per unit charge. Capacitance \(C\) measures how much charge a system can store for a given potential difference. Work \(W\) is energy transferred when a force acts through a displacement. These four ideas are related, but they do not represent the same physical quantity. The main separation is that \(\vec{E}\) is force-based, \(V\) is work-per-charge based, and \(C\) is storage-based.
7. The row that pairs a quantity with its SI unit is:
| Row | Quantity | SI unit |
|---|
| P | Work \(W\) | \(\text{J}\) |
| Q | Charge \(q\) | \(\text{V}\) |
| R | Potential \(V\) | \(\text{F}\) |
| S | Capacitance \(C\) | \(\text{C}\) |
ⓐ. Row R only
ⓑ. Row Q only
ⓒ. Row S only
ⓓ. Row P only
Correct Answer: Row P only
Explanation: Work \(W\) is measured in joule \(\text{J}\), so row P is properly matched. Charge \(q\) is measured in coulomb \(\text{C}\), not volt \(\text{V}\). Potential \(V\) is measured in volt \(\text{V}\), not farad \(\text{F}\). Capacitance \(C\) is measured in farad \(\text{F}\), not coulomb \(\text{C}\). The same letter \(\text{C}\) can appear as the symbol for coulomb and also as the symbol for capacitance \(C\), so the context must be read carefully. A unit name and a quantity symbol should not be confused just because they share a printed letter.
8. The relation \(1\,\text{V}=1\,\_\_\_\_\) is completed by:
ⓐ. \(\text{J C}^{-1}\)
ⓑ. \(\text{C V}^{-1}\)
ⓒ. \(\text{N C}^{-1}\)
ⓓ. \(\text{C J}^{-1}\)
Correct Answer: \(\text{J C}^{-1}\)
Explanation: Potential difference is work done per unit charge. Therefore, the SI unit of potential is joule per coulomb. This gives \(1\,\text{V}=1\,\text{J C}^{-1}\). The unit \(\text{N C}^{-1}\) belongs to electric field \(\vec{E}\), not directly to potential. The unit \(\text{C V}^{-1}\) belongs to capacitance \(C\), because \(C=\frac{Q}{V}\). Reading the unit as “energy per charge” keeps the meaning of volt clear.
9. A charge of \(2\,\text{C}\) is moved between two points, and the work associated with the movement is \(10\,\text{J}\). The potential difference calculated from work per unit charge is:
ⓐ. \(10\,\text{V}\)
ⓑ. \(2\,\text{V}\)
ⓒ. \(20\,\text{V}\)
ⓓ. \(5\,\text{V}\)
Correct Answer: \(5\,\text{V}\)
Explanation: \( \textbf{Given data:} \) Work \(W=10\,\text{J}\) and charge \(q=2\,\text{C}\).
\( \textbf{Required quantity:} \) Potential difference from work per unit charge.
\( \textbf{Meaning used:} \) Potential difference is work divided by charge.
\[
\Delta V=\frac{W}{q}
\]
\( \textbf{Substitution:} \)
\[
\Delta V=\frac{10\,\text{J}}{2\,\text{C}}
\]
\( \textbf{Calculation:} \)
\[
\Delta V=5\,\text{J C}^{-1}
\]
\( \textbf{Unit conversion:} \)
\[
1\,\text{J C}^{-1}=1\,\text{V}
\]
\( \textbf{Final answer:} \) The potential difference is \(5\,\text{V}\).
The value \(20\,\text{V}\) would come from multiplying \(W\) and \(q\), but potential difference uses work per unit charge.
10. If a force does positive work during the displacement of a charge, the energy transfer by that force is:
ⓐ. Zero because electrostatic quantities are scalar
ⓑ. From the force to the moving charge system
ⓒ. Opposite to the displacement in every case
ⓓ. Always independent of the sign of the charge
Correct Answer: From the force to the moving charge system
Explanation: Positive work means that the force contributes energy during the displacement. Negative work means that the force removes energy or opposes the displacement in an energy sense. This sign convention is a prerequisite for understanding potential difference and potential energy. The sign of charge matters later because force direction and energy change can depend on it. A scalar quantity can be positive or negative, so being scalar does not mean being zero. Work signs should be read through energy transfer, not through the symbol alone.
11. In electrostatics, the symbols \(q\), \(q_0\), \(W\), and \(U\) are used with different meanings. The best identification is:
ⓐ. \(q\) is capacitance, \(q_0\) is field, \(W\) is potential, and \(U\) is charge
ⓑ. \(q\) is charge, \(q_0\) is test charge, \(W\) is work, and \(U\) is potential energy
ⓒ. \(q\) is potential difference, \(q_0\) is force, \(W\) is field, and \(U\) is charge density
ⓓ. \(q\) is work, \(q_0\) is potential, \(W\) is charge, and \(U\) is capacitance
Correct Answer: \(q\) is charge, \(q_0\) is test charge, \(W\) is work, and \(U\) is potential energy
Explanation: The symbol \(q\) usually denotes charge, while \(q_0\) commonly denotes a small test charge. Work is represented by \(W\), and electrostatic potential energy is represented by \(U\). These symbols must be kept separate because several electrostatic formulas connect them. For example, work and potential energy have the unit \(\text{J}\), while charge has the unit \(\text{C}\). Potential \(V\) and potential energy \(U\) are also different quantities, even though both are linked with work. Confusing \(V\) with \(U\) hides the factor of charge that connects energy to potential.
12. Assertion: Electrostatic potential can be treated as a scalar quantity.
Reason: Potential at a point describes a work-per-unit-charge idea and does not require a spatial direction.
ⓐ. 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: Electrostatic potential \(V\) is a scalar quantity. Its value may be positive, negative, or zero, but that sign is not a direction in space. Potential is based on work or energy per unit charge, and work is a scalar quantity. Electric field \(\vec{E}\), on the other hand, is a vector because it has a definite direction of force on a positive test charge. The Reason gives the correct basis for why potential is not treated like a vector. The sign of \(V\) should be handled algebraically, while the direction information is carried by \(\vec{E}\).
13. A capacitor has charge \(Q\) on one plate and potential difference \(V\) between its plates. The quantity \(\frac{Q}{V}\) represents:
ⓐ. Potential energy stored per unit charge
ⓑ. Electric field between the plates
ⓒ. Work done by the field per metre
ⓓ. Capacitance of the capacitor
Correct Answer: Capacitance of the capacitor
Explanation: Capacitance is defined as charge stored per unit potential difference. The relation is \(C=\frac{Q}{V}\), where \(Q\) is the magnitude of charge on either plate and \(V\) is the potential difference. Its SI unit is \(\text{F}\), where \(1\,\text{F}=1\,\text{C V}^{-1}\). Electric field involves force per unit charge or potential gradient, not simply \(\frac{Q}{V}\). Potential energy per unit charge would have the unit \(\text{J C}^{-1}\), which is \(\text{V}\). Capacitance tells how much charge storage is obtained for a given potential difference.
14. A circuit component is marked as having a large capacitance. Without going into its construction, this means it can:
ⓐ. Store more charge for the same potential difference
ⓑ. Remove the need for an insulating gap
ⓒ. Turn scalar potential into vector electric field
ⓓ. Make the potential difference zero in every circuit
Correct Answer: Store more charge for the same potential difference
Explanation: A larger capacitance means a larger value of \(C=\frac{Q}{V}\). For the same potential difference \(V\), a capacitor with larger \(C\) can store a larger charge \(Q\). This statement is about charge storage, not about making \(V\) always zero. A capacitor still needs separation by an insulating medium, otherwise charges would flow directly between conductors. The electric field between plates is related to the stored charges and potential difference, but capacitance itself is not a vector. The phrase “large capacitance” should be read as greater charge storage ability under the same voltage condition.
15. A point has potential \(+8\,\text{V}\), and another point has potential \(-8\,\text{V}\), both relative to the same reference level. The two values show:
ⓐ. Zero potential difference between the two points
ⓑ. Equal magnitudes with opposite algebraic signs
ⓒ. Equal electric field directions at the two points
ⓓ. Equal forces on every possible charge placed there
Correct Answer: Equal magnitudes with opposite algebraic signs
Explanation: The values \(+8\,\text{V}\) and \(-8\,\text{V}\) have the same magnitude but opposite signs. Since potential is scalar, these signs are algebraic and do not themselves indicate two opposite directions. The electric field at those points cannot be decided from potential values alone without knowing how \(V\) changes in space. A charge placed at the two points may have different potential energies because \(U=qV\) depends on both \(q\) and \(V\). The potential difference between the two points is not zero; the two potentials differ by \(16\,\text{V}\). Equal magnitude of scalar potential is not the same as equal vector field.
16. Identify the properly classified set of quantities.
ⓐ. \(V\) vector, \(C\) scalar, \(\vec{E}\) scalar, \(\vec{F}\) vector
ⓑ. \(V\) scalar, \(C\) scalar, \(\vec{E}\) vector, \(\vec{F}\) vector
ⓒ. \(V\) scalar, \(C\) vector, \(\vec{E}\) vector, \(\vec{F}\) scalar
ⓓ. \(V\) vector, \(C\) vector, \(\vec{E}\) scalar, \(\vec{F}\) scalar
Correct Answer: \(V\) scalar, \(C\) scalar, \(\vec{E}\) vector, \(\vec{F}\) vector
Explanation: Electrostatic potential \(V\) is scalar because it has no direction attached to it. Capacitance \(C\) is also scalar because it measures charge stored per unit potential difference. Electric field \(\vec{E}\) is a vector because it gives the direction of force on a positive test charge. Force \(\vec{F}\) is a vector because it has both magnitude and direction. Signs on scalar quantities are not the same as vector directions. This classification helps separate energy-related quantities from force-related quantities.
17. Three statements about basic electrostatic quantities are given.
I. Potential difference has the unit \(\text{J C}^{-1}\).
II. Capacitance has the unit \(\text{C V}^{-1}\).
III. Electric field is measured directly in \(\text{F}\).
The supported statements are:
ⓐ. I, II, and III
ⓑ. I and III only
ⓒ. I and II only
ⓓ. II and III only
Correct Answer: I and II only
Explanation: Statement I is supported because \(1\,\text{V}=1\,\text{J C}^{-1}\). Statement II is supported because capacitance is \(C=\frac{Q}{V}\), so its unit is \(\text{C V}^{-1}\), called farad \(\text{F}\). Statement III is not supported because \(\text{F}\) is the unit of capacitance, not electric field. Electric field is commonly measured in \(\text{N C}^{-1}\), and it is also equivalent to \(\text{V m}^{-1}\) in later relations. The symbol \(\text{F}\) should be read as farad in this context, not as force. Unit matching is safest when the defining relation is checked.
18. A slow movement of charge is considered between two points in an electrostatic field. Why is the idea of work useful before introducing detailed formulas?
ⓐ. It proves that capacitance and potential are the same quantity
ⓑ. It removes the need to know the sign of charge
ⓒ. It connects force effects with energy and potential difference
ⓓ. It changes electric field from vector to scalar everywhere
Correct Answer: It connects force effects with energy and potential difference
Explanation: Work links force and displacement with energy transfer. In electrostatics, this connection lets us describe potential and potential difference through work per unit charge. Electric field \(\vec{E}\) gives the force side of the description, while potential \(V\) gives the work or energy side. The sign of charge still matters in later work and energy relations, so work does not remove sign reasoning. Capacitance \(C\) is related to \(Q\) and \(V\), but it is not the same as potential. Work provides the bridge between field ideas and energy ideas in electrostatics.
19. A record shows that \(6\,\text{J}\) of external work is needed to bring a small positive test charge of \(3\,\text{C}\) from the reference point to a point \(P\). The electrostatic potential at \(P\) is:
ⓐ. \(3\,\text{V}\)
ⓑ. \(18\,\text{V}\)
ⓒ. \(9\,\text{V}\)
ⓓ. \(2\,\text{V}\)
Correct Answer: \(2\,\text{V}\)
Explanation: \( \textbf{Given data:} \) External work \(W_{\text{ext}}=6\,\text{J}\) and test charge \(q_0=3\,\text{C}\).
\( \textbf{Required quantity:} \) Electrostatic potential \(V\) at point \(P\).
\( \textbf{Definition used:} \) Potential is external work done per unit positive test charge.
\[
V=\frac{W_{\text{ext}}}{q_0}
\]
\( \textbf{Substitution:} \)
\[
V=\frac{6\,\text{J}}{3\,\text{C}}
\]
\( \textbf{Calculation:} \)
\[
V=2\,\text{J C}^{-1}
\]
\( \textbf{Unit relation:} \)
\[
1\,\text{J C}^{-1}=1\,\text{V}
\]
\( \textbf{Final answer:} \) The potential at \(P\) is \(2\,\text{V}\).
The value \(18\,\text{V}\) would come from multiplying work and charge, but potential uses work per unit charge.
20. A negative value of electrostatic work is mentioned while discussing movement of a charge. The sign most directly means that:
ⓐ. The potential must have no reference level
ⓑ. The electric field has changed into capacitance
ⓒ. The force opposes the displacement energetically
ⓓ. The moving charge has become electrically neutral
Correct Answer: The force opposes the displacement energetically
Explanation: Negative work means that the force considered is opposing the displacement in the energy sense. It does not mean that charge disappears or becomes neutral. Work is a scalar quantity, so it can have positive, negative, or zero value depending on force and displacement. In electrostatics, this sign becomes important when connecting work with potential difference and potential energy. A negative work value must be read with the specified force, such as external force or electrostatic force. The sign of work is about energy transfer, not about removing the electric nature of the charge.
