CUET UG Physics Booster Test – 2 Electrostatic Potential Foundations

For a system acted upon only by conservative forces such as gravitational or spring forces, the total mechanical energy remains conserved. Mechanical energy is defined as the sum of kinetic energy and potential energy. Therefore, Ki + Ui = Kf + Uf This equation states that any decrease in potential energy is accompanied by an equal increase in kinetic energy, and vice versa. The total energy of the system remains constant throughout the motion. This principle is known as the law of conservation of mechanical energy and is a fundamental concept discussed in NCERT. For example, when a body falls under gravity, potential energy decreases while kinetic energy increases by the same amount. Hence, the sum remains unchanged. Thus, the correct answer is D Ki + Ui = Kf + Uf.

When work is done against a spring, elastic potential energy is stored in the spring. Once the external force is removed, the restoring force of the spring acts on the body. The stored potential energy begins converting into kinetic energy. According to the conservation of mechanical energy, the decrease in spring potential energy is exactly equal to the increase in kinetic energy, provided non-conservative forces such as friction are absent. The body therefore starts moving, gaining kinetic energy while losing an equal amount of elastic potential energy. This energy transformation continues as the spring oscillates. Thus, the correct answer is A the body moves, gaining kinetic energy and losing an equal amount of potential energy.

In a gravitational field, the potential energy of a body is given by U = mgh where m is mass and gh represents gravitational potential. In electrostatics, the analogous quantity is electric potential V. Replacing mass by charge q and gravitational potential gh by electric potential V gives U = qV This relation shows that the electrostatic potential energy of a charge depends on both the charge and the electric potential at the point. NCERT frequently draws an analogy between gravitational and electrostatic fields to explain potential energy concepts. Just as mass placed at a gravitational potential possesses potential energy, a charge placed at an electric potential possesses electrostatic potential energy. Thus, the correct answer is B qV.

When a positive charge q is brought closer to another positive charge Q, work must be done against the repulsive electrostatic force. This work gets stored as electrostatic potential energy. After the external force is removed, only the repulsive electric force acts on the charge. The charge begins moving away from Q, and the stored potential energy decreases. According to conservation of energy, this decrease in potential energy appears as an increase in kinetic energy. Thus, the stored electrostatic potential energy at point P acts as a source of kinetic energy for the moving charge. This is analogous to releasing a compressed spring, where stored energy converts into motion. Therefore, the correct answer is B the stored potential energy at P is used to provide kinetic energy to charge q.

When a positive charge q is slowly moved towards another positive charge Q, the displacement is towards Q. Since like charges repel, the electric force on q acts away from Q, opposite to the displacement. Work done by a force is positive when force and displacement are in the same direction and negative when they are in opposite directions. The external force must be applied towards Q to overcome the repulsive electric force. Therefore, the external force and displacement are in the same direction, making the work done by the external force positive. The electric force acts opposite to the displacement, so the work done by the electric force is negative. Hence, External Force → Positive Work Electric Force → Negative Work Thus, the correct answer is C Positive, Negative.

When a charge is moved from R to P, the change in potential energy is given by ΔU = UP − UR = WRP where WRP is the work done by the external force. The work done by the electric field is equal in magnitude but opposite in sign. Work done by electric field = −WRP Since the electrostatic field is conservative, the work done depends only on the initial and final positions and not on the path followed. Therefore, the proper matching becomes: 1 → c 2 → a 3 → b 4 → d These relationships form the foundation of the definition of electric potential energy in NCERT.

A conservative force field possesses the property that work done depends only on the initial and final positions of the particle. This immediately implies that the total work done over any closed path is zero. Because of this path independence, a potential energy function can be defined. Electrostatic forces satisfy all these conditions and therefore allow the concepts of electric potential and electric potential energy. Statement 4 is incorrect because ΔU depends only on the end points and not on the path taken. Hence Statements 1, 2 and 3 are correct while Statement 4 is false. Thus, the correct answer is A 1, 2 and 3 are correct.

Coulomb's law describes the force between stationary charges and follows an inverse-square dependence on distance. Like gravitational force, the electrostatic force is conservative in nature. This means the work done by the force depends only on the initial and final positions and not on the path followed. Using Coulomb's law, one can mathematically prove that electrostatic work is path independent. This property allows the definition of electric potential energy and electric potential. Statement C is incorrect because Coulomb force is not non-conservative; it is a classic example of a conservative force similar to gravity. Thus, the correct answer is C It differs from the gravitational force law as the Coulomb force is strictly non-conservative.

Potential energy can be shifted by adding an arbitrary constant α to all values without affecting any physical prediction. Such a shift changes the absolute value of potential energy at every point. However, the physically meaningful quantity is the potential energy difference. If α is added everywhere, (UP + α) − (UR + α) = UP − UR The constant cancels completely. Therefore, potential energy differences remain unchanged. Path independence is a property of the conservative force field and is unaffected by adding a constant. Hence Statements 1 and 3 are correct, while Statements 2 and 4 are incorrect. Thus, the correct answer is B 1 and 3 are correct.

In electrostatics, the absolute value of potential energy is not uniquely defined because an arbitrary constant may be added to it. Therefore, the quantity that has physical meaning is the difference in potential energy between two points. When a charge moves from point A to point B, the relevant quantity is ΔU = UB − UA This energy difference determines the work done and the energy transfer involved in the process. It remains unchanged even if a constant is added to all potential energy values. NCERT emphasizes that potential energy differences, not absolute values, are measurable and physically significant. Thus, the correct answer is A (UB − UA).

In electrostatics, potential energy is defined only up to an arbitrary constant. For convenience, NCERT chooses the potential energy of a charge to be zero at infinity. This choice provides a unique reference point for calculating potential energy at any finite location. Once this reference is established, the potential energy of a charge at a point becomes equal to the work done by an external agent in bringing the charge slowly from infinity to that point against the electrostatic force. Mathematically, UP = W∞→P This convention simplifies calculations and allows a consistent definition of electrostatic potential and potential energy. It does not make potential energy infinite, nor does it affect potential differences between finite points. Thus, the correct answer is B the definition of potential energy of a charge at any point becomes equal to the work done in bringing it from infinity to that point.

When a charge is brought slowly from infinity to a point in an electric field, the work done by the external force is stored as electrostatic potential energy. Since the charge is moved slowly, there is no change in kinetic energy. Given: Work done by external force = 10 J Potential energy at infinity = 0 Therefore, UP = Wexternal UP = 10 J The value of the charge (2 C) is not required because the question directly provides the work done. The potential energy gained by the charge is exactly equal to the work performed by the external agent. Thus, the correct answer is D 10 J.

Electrostatic potential is defined as the work done per unit positive test charge in bringing it from infinity to a given point. Although a test charge is used in the definition, the resulting value of potential is independent of the magnitude of the test charge. This is because both work done and charge change proportionally, leaving their ratio constant. V = W/q Therefore, electrostatic potential is a characteristic of the electric field created by the source charge configuration. It depends only on the arrangement and magnitudes of the source charges and not on the charge used for measurement. Hence, the correct answer is B) is a characteristic of the electric field associated purely with the source charge configuration.

Electrostatic potential energy is given by U = qV Since potential energy contains q directly, it depends on the magnitude of the test charge. Electrostatic potential is defined as V = U/q or work done per unit charge. Therefore, the value of potential remains independent of the test charge used. This distinction is important in electrostatics. Potential energy changes if the charge changes, but the potential at a point remains fixed for a given source-charge configuration. Therefore: Dependent on q → Potential Energy Independent of q → Potential Thus, the correct answer is B Potential Energy, Potential.

Luigi Galvani observed contractions in frog muscles and proposed that electricity originated from special properties of animal tissue. This idea became known as animal electricity. Alessandro Volta disagreed and suggested that electricity was generated when a moist conductor was placed between dissimilar metals. His investigations eventually led to the construction of the voltaic pile, the first practical battery capable of producing a continuous electric current. The term animal electricity refers to electrical phenomena associated with living tissue and was central to the historical debate between Galvani and Volta. Thus, the correct matching is: 1 → b 2 → a 3 → c 4 → d Therefore, the correct answer is B) 1-b, 2-a, 3-c, 4-d.

The first voltaic pile was invented by Alessandro Volta and is regarded as the first practical battery capable of producing a continuous electric current. It consisted of alternating layers of two different metals separated by moist cardboard or cloth soaked in an electrolyte solution. Statement 1 is correct because Volta was the inventor of the voltaic pile. Statement 2 is also correct because moist cardboard functioned as the electrolyte layer. Statement 3 is incorrect because the pile used dissimilar metals, such as zinc and copper, rather than identical metals. Statement 4 is incorrect because Volta's work demonstrated that electricity could be generated without relying on any exceptional properties of frog muscle tissue. Therefore, Statements 1 and 2 are correct. Thus, the correct answer is A 1 and 2 are correct.

To define electrostatic potential accurately, an infinitesimal test charge dq is used. The purpose of choosing such a small charge is to ensure that it does not alter the original charge configuration responsible for producing the electric field. Potential is defined through the ratio dW/dq, where dW is the infinitesimal work done by an external force in moving the charge. During the motion, the external force is applied equal and opposite to the electrostatic force so that the charge moves slowly without acceleration. Statement B is incorrect because the test charge is intentionally chosen to be extremely small. It should not exert a large force capable of rapidly moving the source charges. Thus, the correct answer is B It exerts an equal and opposite massive force, rapidly moving the source charges.

In electrostatic measurements, the source charge configuration must remain unchanged while the test charge is moved. This ensures that the electric field being measured remains constant. Statement 1 is correct because the source charge Q is assumed fixed. Statement 2 is correct because an external or unspecified force may conceptually hold the source charge in place if interactions become significant. Statement 4 is also correct because any disturbance of the source configuration changes the electric field and invalidates the measurement. Statement 3 is incorrect because the test charge should be moved infinitesimally slowly, not violently accelerated. Slow motion prevents kinetic energy changes and ensures accurate determination of potential. Thus, the correct answer is C 1, 2 and 4 are correct.

The electric force acting on a positive test charge dq in an electric field E is FE = dqE To move the charge slowly without acceleration, the external force must exactly oppose the electric force. Therefore, Fext = -dqE The infinitesimal work done by the external agency over displacement dr is dW = Fext · dr Substituting the expression for external force, dW = -dq(E) · dr This relation is fundamental in deriving electrostatic potential and potential difference in NCERT. Thus, the correct answer is D -dq(E) · dr.

When defining electrostatic potential and potential energy, NCERT assumes that the test charge is moved with infinitesimally slow constant speed. This condition ensures that the charge experiences no acceleration. According to Newton's second law, zero acceleration means that the net force on the charge is zero. Consequently, there is no change in kinetic energy during the motion. Under these conditions, all the work done by the external force is stored entirely as electrostatic potential energy. This makes it possible to define potential energy and potential difference accurately. Any motion involving acceleration would change kinetic energy and complicate the energy accounting. Thus, the correct answer is B) must be brought with infinitesimally slow constant speed.