CUET UG Physics Booster Test – 3 Electrostatic Potential Foundations

When a charge is moved slowly from point R to point P in an electrostatic field, the external force applied is equal in magnitude and opposite in direction to the electric force. Since the charge moves with infinitesimally slow constant speed, there is no change in kinetic energy. According to the work-energy principle, ΔK = Wext + WE Since ΔK = 0, Wext + WE = 0 This means that the work done by the external force is exactly equal and opposite to the work done by the electric force. The positive work done by the external force is stored as potential energy, while the electric field performs an equal amount of negative work. Thus, the correct answer is A. Wext + WE = 0.

While the external force is applied, energy is stored in the system as electrostatic potential energy. If the external force is suddenly removed, the electrostatic force becomes the only force acting on the charge. Since electrostatic force is conservative, the stored potential energy begins converting into kinetic energy. As the charge moves under the influence of the electric field, its kinetic energy increases while potential energy decreases by an equal amount. The total mechanical energy, Mechanical Energy = Kinetic Energy + Potential Energy remains constant throughout the motion. This is a direct consequence of conservation of mechanical energy in conservative force fields. Therefore, the stored potential energy supplies kinetic energy to the charge while total energy remains conserved. Thus, the correct answer is C. the stored potential energy is used to provide kinetic energy to the charge while total energy remains conserved.

For two point charges, U ∝ 1/r where U is electrostatic potential energy and r is the separation between the charges. If the distance is tripled, r' = 3r Then, U' ∝ 1/(3r) U' = U/3 Thus, the electrostatic potential energy becomes one-third of its original value. The question reminds us that force varies as 1/r², but potential energy varies as 1/r. Therefore, the reduction factor for energy is different from that for force. Hence, when the separation is tripled, the electrostatic potential energy decreases to one-third of its original value. Thus, the correct answer is B. It decreases to 1/3 of its original value.

Work done by a force is given by the dot product of force and displacement. W = F · s When a positive charge is moved against the direction of the electric force, the displacement is opposite to the force. Therefore, the angle between force and displacement is 180°, making the work done by the electric field negative. This negative work corresponds to an increase in potential energy of the system. Such situations commonly occur when an external agent pushes a charge against a repulsive electrostatic force. Therefore, for the work done by the electric field to be negative, displacement must occur opposite to the electric force. Thus, the correct answer is D. the displacement must be in an opposite sense to the electric force for the work done by the electric field to be negative.

When a positive test charge is moved against an electrostatic force, an external force is applied in the direction of displacement. Therefore, the external force and displacement vectors are parallel. The electric force acts opposite to the intended displacement because the charge is being pushed against the field. Hence, the electric force and displacement vectors are antiparallel. This arrangement ensures that the external force performs positive work while the electric field performs negative work. The charge is moved slowly so that the two forces balance each other and no acceleration occurs. Thus: External force & displacement → Parallel Electric force & displacement → Antiparallel Therefore, the correct answer is A. Parallel, Antiparallel.

In electrostatics, the change in potential energy when a charge moves from R to P is given by UP − UR = WRP where WRP is the work done by the external force. The corresponding potential difference is defined as VP − VR = WRP/q Thus, potential difference is simply the work done per unit charge. Potential energy difference represents the total energy change, whereas potential difference represents energy change per unit charge. Therefore, 1 → a 2 → b 3 → c 4 → d These relations are fundamental to the NCERT definitions of electrostatic potential energy and electrostatic potential.

The path independence of electrostatic work follows from the conservative nature of Coulomb's force. Since Coulomb's force is an inverse-square central force, the work done between two points depends only on the initial and final positions. Because work is path independent, potential energy can be defined as a state function. This means the value of potential energy depends only on the state of the system and not on the path used to reach that state. Statement 3 is incorrect because the external force need not be non-conservative. It is simply applied to balance the electric force during slow displacement. Thus, Statements 1, 2 and 4 are correct. Therefore, the correct answer is A. 1, 2 and 4 are correct.

Electrostatic fields produced by static charges are conservative. Their field lines originate from positive charges and terminate on negative charges; they do not form closed loops. The path independence of electrostatic work can be mathematically established using Coulomb's law and vector calculus. This proof confirms that electrostatic force is conservative and that the work done depends only on the initial and final positions. Statement B is incorrect because closed continuous loops are characteristic of certain magnetic field lines, not electrostatic field lines. Therefore, the correct answer is B. It relies on the fact that electric fields due to static charges form closed continuous loops.

Potential energy is not uniquely defined because an arbitrary constant can be added to all potential energy values. Therefore, the absolute value of potential energy is physically undetermined. Only potential energy differences can be measured experimentally because they determine work done and energy transfer. If the zero-point reference is shifted by a constant amount, all potential energies change equally, but the differences remain unchanged. Statement 3 is incorrect because adding a constant does not affect the potential gradient. Gradients depend on differences, and constants disappear during differentiation. Thus, Statements 1, 2 and 4 are correct. Therefore, the correct answer is B. 1, 2 and 4 are correct.

Suppose the potential energies at two points are U1 and U2. The potential energy difference is ΔU = U2 − U1 = x If the reference level is shifted by adding a constant y to every potential energy value, the new energies become U1 + y and U2 + y The new potential energy difference becomes (U2 + y) − (U1 + y) = U2 − U1 = x The constant y cancels completely. Therefore, changing the zero reference level does not alter the measured potential energy difference. This is why only energy differences have physical significance in electrostatics. Thus, the correct answer is C. x.

Electrostatic potential energy is defined only up to an arbitrary additive constant. Therefore, a reference point must be chosen. In electrostatics, infinity is commonly selected because the Coulomb force and interaction energy become negligibly small as the separation between charges approaches infinity. This choice simplifies calculations and allows potential energy at any point to be defined as the work done in bringing a charge from infinity to that point. It is a convention rather than a mathematical necessity. Thus, the correct answer is D. a convenient choice because the Coulomb interaction inherently vanishes at infinite separation.

The work done by an external force in bringing a charge from infinity to a point is equal to the change in electrostatic potential energy. Using U = qV Given: q = -3 C V = 200 V Therefore, U = (-3)(200) U = -600 J Since the potential energy at infinity is taken as zero, the work done by the external force equals the final potential energy. Hence, W = -600 J The negative sign indicates that the system loses potential energy because a negative charge is brought to a region of positive potential. Thus, the correct answer is C -600 J.

Electrostatic potential is defined as the work done per unit positive test charge in bringing it from infinity to a given point. By dividing the work done by the test charge, the dependence on the test charge magnitude is removed. The resulting quantity depends only on the source charge configuration and the electric field it produces. Therefore, electrostatic potential becomes a property of the field itself rather than of the test charge used to measure it. This is why electrostatic potential is regarded as a characteristic of the electric field associated with the source charges. Thus, the correct answer is B. the resulting quantity represents a characteristic of the electric field associated purely with the source charge configuration.

Potential energy has the same dimensions as work and energy: [Potential Energy] = [M¹ L² T⁻²] Electrostatic potential is defined as energy per unit charge: V = U/q The dimension of charge is [Q] = [AT] Therefore, [V] = [M¹ L² T⁻²]/[AT] = [M¹ L² T⁻³ A⁻¹] Hence, the dimensions are: Potential Energy → [M¹ L² T⁻²] Potential → [M¹ L² T⁻³ A⁻¹] Thus, the correct answer is A.

Luigi Galvani concluded from his frog-leg experiments that electricity originated from a special property of animal tissue. Alessandro Volta disagreed and proposed that electricity was produced by the interaction of dissimilar metals separated by a moist conducting medium. Volta's structural innovation was the voltaic pile, a large stack of alternating metal disks separated by moist cardboard. This device became the first practical battery capable of producing a continuous electric current. Therefore: 1 → b 2 → a 3 → c 4 → d This matching accurately reflects the historical development of electricity discussed in NCERT.

The first voltaic pile was invented by Alessandro Volta and is considered the first practical battery. It consisted of alternating disks of dissimilar metals such as zinc and copper. Between these metal disks were moist cardboard or cloth separators soaked in an electrolyte solution. The metal disks functioned as electrodes, while the moist cardboard provided ionic conduction necessary for the chemical reactions producing electric current. Frog muscle tissue was associated with Galvani's experiments on animal electricity and was not a component of Volta's battery. Therefore, Statements 1, 2 and 4 are correct, while Statement 3 is incorrect. Thus, the correct answer is A. 1, 2 and 4 are correct.

In defining electrostatic potential, the test charge dq is assumed to be infinitesimally small. This ensures that it does not disturb the source charges responsible for creating the electric field. The electric field and potential being measured therefore remain unchanged. The limit dq → 0 is introduced only to avoid modifying the original charge configuration. It does not imply that the potential itself becomes zero. Electrostatic potential is a property of the source charges and can have any value depending on the charge distribution. Therefore, Statement C is incorrect because the value of potential does not become universally zero when dq approaches zero. Thus, the correct answer is C. It mathematically ensures the potential V at the point becomes universally zero.

During the definition of electrostatic potential, the source charge configuration is assumed fixed. If the source charge Q were allowed to move, the separation distance r would change continuously, altering the electric field and potential being measured. According to Newton's Third Law, the test charge q exerts an equal and opposite Coulomb force on Q. Therefore, in theory, an unspecified external force is assumed to hold Q fixed against this force. Statement 3 is incorrect because holding Q fixed does not violate conservation of mechanical energy. It is simply an idealized condition used to define the field and potential. Therefore, Statements 1, 2 and 4 are correct. Thus, the correct answer is B. 1, 2 and 4 are correct.

The electric force acting on the charge is FE = qE To move the charge infinitesimally slowly, an external force of equal magnitude and opposite direction is applied. Fext = -qE Therefore, Fnet = FE + Fext = qE + (-qE) = 0 Since the net force is zero, the acceleration is also zero. This condition ensures that there is no change in kinetic energy and that all external work contributes to changing potential energy. Thus, the correct answer is D. 0.

The definition of electrostatic potential energy assumes that the charge is moved infinitesimally slowly so that there is no change in kinetic energy. This requires the external force to exactly balance the electrostatic force. If the external force becomes greater than the opposing electric force, a non-zero net force acts on the charge. According to Newton's second law, this net force causes acceleration and increases the kinetic energy of the charge. As a result, part of the work done by the external force goes into kinetic energy rather than entirely into potential energy. This violates the strict condition used in defining potential energy difference. Therefore, the correct answer is B. the charge would acquire kinetic energy, violating the strict definition of potential energy difference.