CUET UG Physics Booster Test – 2 Electric Field and Dipoles

The force between charges is directly described by Coulomb's law; therefore 1 → a. The electric field at a point is a characteristic of the source-charge configuration and is independent of the test charge used to measure it. Thus 2 → b. Electric field is defined as the force experienced by a unit positive test charge. Hence 3 → c. The force acting on a charge q placed in an electric field E is: Therefore 4 → d. Combining all correct correspondences gives: 1-a, 2-b, 3-c, 4-d. This matching summarizes the fundamental relationships among Coulomb force, electric field and force on a test charge discussed in NCERT.

According to electromagnetic theory, changes in electric and magnetic fields propagate through space at the speed of light, not instantaneously. Accelerated charges produce electromagnetic waves, making Statement 2 correct. The electric field concept provides a physical explanation for the delay between a changing charge configuration and the observation of its effects elsewhere, so Statement 3 is correct. Electromagnetic fields possess independent dynamics and can transport energy through space, as seen in electromagnetic radiation. Therefore Statement 4 is also correct. Statement 1 is incorrect because information cannot travel instantaneously between distant charges. Thus Statements 2, 3 and 4 are correct.

The force on a charge in an electric field is: Given: Substituting: Unit Verification Therefore the magnitude of the force acting on the electron is: Hence Option D is correct.

The electric field is defined operationally as: Therefore Statement 2 is correct. The source charge configuration must remain unchanged while measuring the field. This requires the test charge to be extremely small, making Statement 1 correct. When q approaches zero, the force exerted by the test charge on the source charges becomes negligible, so the source charge remains essentially undisturbed. Hence Statement 4 is correct. Statement 3 is incorrect because electric field depends on source charges and position, not on the magnitude of the test charge. Thus Statements 1, 2 and 4 are correct.

The electric field due to a point charge Q located at the origin is given by: where: • r is the distance from the charge. • is the radial unit vector. The magnitude follows the inverse-square law and the direction is outward for a positive charge. The unit vector is necessary because electric field is a vector quantity. Therefore the complete vector expression is: Hence Option B is correct.

For a negative point charge, the electric field at every point is directed radially inward because a positive test charge experiences an attractive force toward the source. Therefore, Statement A is correct. Since the force on a positive test charge is directed toward the negative charge, Statement B is also correct. The field of a point charge depends only on the radial distance from the charge and not on direction, giving spherical symmetry. Hence Statement D is correct. The incorrect statement is C. Electric field lines do not originate from a negative charge. By convention, field lines originate from positive charges and terminate on negative charges. Therefore, field lines associated with a negative charge point inward and end on the charge. Hence Option C is correct.

For discrete charges, the total electric field is obtained by vector addition of individual electric fields according to the superposition principle. When the charge distribution is continuous, it is divided into infinitesimally small charge elements dq. Each element produces a small electric field dE. The total field is then obtained by integrating all contributions: Thus, the discrete vector summation is replaced by integration over the entire charge distribution. This approach is fundamental in calculating fields due to charged rods, rings, discs and other continuous distributions. Hence Option B is correct.

The electric field due to a point charge is: The field magnitude depends only on the distance r from the charge. All points on a sphere centered at the charge have the same radius r. Therefore, every point on that sphere experiences the same electric field magnitude. This property is called spherical symmetry. Statement A is incorrect because the dependence is on 1/r², not 1/r. Statement C is incorrect because the field magnitude is independent of angular position. Statement D is opposite to the actual inverse-square law. Hence Option B is correct.

Electric field is a property of the source-charge configuration. For a point charge, showing that E depends on the source charge Q and position r. A test charge is used only to measure the field through the relation: Although the force F changes with q, the ratio F/q remains constant. Therefore, the electric field is independent of the magnitude of the test charge. This distinction is central to the NCERT definition of electric field. Hence Option C is correct.

According to electromagnetic theory, changes in the motion of a charge produce changes in the surrounding electromagnetic field. These changes do not reach distant points instantaneously. Instead, they propagate through space at the speed of light: This finite propagation speed explains the time delay between cause and effect in electromagnetic interactions. NCERT emphasizes that the field concept naturally accounts for this delay and avoids the idea of instantaneous action at a distance. Therefore, the maximum speed at which information about the accelerated motion of q₁ can reach q₂ is the speed of light. Hence Option C is correct.

For a point charge, electric field lines spread uniformly in all directions. Consider an imaginary spherical surface of radius r centered on the charge. The total number of field lines crossing any such sphere remains constant because the source charge is unchanged. The area of the spherical surface is: As the distance from the charge increases, the same number of field lines is distributed over a larger area. Therefore, the number of field lines crossing a unit area decreases inversely with the square of the distance. Thus, This is consistent with the inverse-square variation of electric field strength around a point charge. Hence Option D is correct.

A fundamental property of electrostatic field lines is that no two field lines can intersect. At any point in space, the electric field has one unique direction. If two field lines crossed, the tangent at the intersection would indicate two different directions for the electric field. This is physically impossible because the electric field vector at a point must have a unique direction. Therefore Statements A, B and D correctly explain why field lines cannot cross. Statement C is incorrect because crossing field lines do not imply infinite field strength. The real reason crossing is impossible is the violation of uniqueness of field direction. Hence Option C is correct.

The concept of solid angle helps explain the distribution of electric field lines around a point charge. For a given solid angle, the intercepted area on a spherical surface grows as r². Since the total number of field lines associated with a charge remains constant, these lines become more spread out as distance increases. Consequently, the number of field lines crossing a unit area decreases according to: This result directly supports the inverse-square dependence of electric field magnitude around a point charge. Thus, the density of field lines is inversely proportional to r². Hence Option A is correct.

Electrostatic field lines originate from positive charges and terminate on negative charges or at infinity. Therefore Statement 4 is correct. Electrostatic fields are conservative in nature. As a consequence, electrostatic field lines do not form closed loops. This makes Statements 1 and 2 correct. Field lines are continuous curves and cannot suddenly break in a region where no charge exists. Therefore Statement 3 is incorrect. NCERT emphasizes that electrostatic field lines provide a continuous representation of the electric field and always indicate a unique direction at every point. Hence Statements 1, 2 and 4 are correct.

An electric dipole consists of two equal and opposite charges separated by a small distance. Since the charges have equal magnitudes and opposite signs, the total charge of the dipole is zero, making Statement 1 correct. At distances much larger than the separation between the charges, the electric fields due to +q and −q partially cancel, causing the dipole field to become much weaker. Thus Statement 3 is correct. The dipole moment vector is directed from the negative charge toward the positive charge, making Statement 4 correct. Statement 2 is incorrect because although the net charge is zero, the electric field of a dipole is not zero everywhere. A dipole produces a finite electric field throughout space. Hence Statements 1, 3 and 4 are correct.

A polar molecule is one in which the centers of positive and negative charges do not coincide. Because of this separation, the molecule possesses a permanent electric dipole moment even when no external electric field is applied. Examples include molecules such as HCl and H₂O. In these molecules, the charge distribution is naturally asymmetric, producing a non-zero dipole moment. The dipole moment is directed from the center of negative charge toward the center of positive charge. Since the charge centers are separated, the molecule behaves like a permanent dipole. Therefore, the correct description of a polar molecule is that the centers of positive and negative charges do not coincide and a permanent dipole moment exists. Hence Option C is correct.

For a short electric dipole, the electric field on the axial line at large distances is given by: Therefore, 1 → d. The electric field on the axial line is directed along the dipole moment vector p. Hence, 2 → c. An electric dipole consists of equal and opposite charges +q and −q. Therefore, the net charge of the dipole is zero, giving 3 → a. A point dipole is obtained in the limiting case when: such that remains finite. Hence, 4 → b. Therefore, the correct matching is: 1-d, 2-c, 3-a, 4-b. This matching directly follows the NCERT definitions and formulas for electric dipoles and their axial electric fields.

For a short electric dipole, the electric field expressions are: Axial field: Equatorial field: Both expressions contain the factor: This indicates that the dipole field decreases inversely with the cube of the distance from the dipole. This is different from a single point charge whose field decreases as 1/r². Hence Option C is correct.

For a short dipole: Axial field: Equatorial field: Comparing: The question states that the axial field magnitude equals E. Therefore: Hence the electric field on the equatorial plane is half the field on the axial line at the same distance. Thus Option D is correct.

At a point on the equatorial plane of a dipole, the electric fields due to +q and −q have equal magnitudes. Resolving these fields into components: • Components perpendicular to the dipole axis are equal and opposite and therefore cancel. • Components along the dipole axis are in the same direction and add together. The resultant electric field points opposite to the dipole moment vector p. Therefore the final equatorial field is: directed opposite to p̂. Hence Option B is correct.