CUET UG Physics Booster Test – 3 Electric Field and Dipoles

Modern electromagnetic theory treats electric and magnetic fields as physically real entities rather than mere mathematical devices. Although fields are often detected through the forces they exert on charges, they possess an existence independent of the charges used to observe them. NCERT explains that electromagnetic fields have their own dynamics and evolve according to Maxwell's laws. They can transport energy through space in the form of electromagnetic waves. Even after a source is switched off, previously generated electromagnetic disturbances continue to propagate through space. Therefore, Statements B, C and D correctly describe the physical reality of electromagnetic fields. Statement A is incorrect because fields are not merely mathematical constructs; they are real physical entities capable of carrying energy and momentum. Hence Option A is correct.

The classical idea of action at a distance assumes that one charge can influence another instantaneously regardless of separation. However, according to modern physics, no information or physical influence can travel faster than the speed of light. When a charge accelerates, changes in its electromagnetic field propagate outward at speed c. These changes reach distant charges after a finite time delay. The field concept naturally explains this finite propagation time. Instead of instantaneous interaction, the source modifies the surrounding field, and the disturbance travels through space before affecting another charge. Therefore, the field picture is essential for understanding interactions between accelerating charges. Hence Option D is correct.

The operational definition of electric field requires that the source charge distribution remains essentially unchanged while the field is being measured. When a test charge is introduced near a charged planar sheet, it exerts a force on the charges of the sheet. However, these source charges remain effectively fixed because they are held in place by internal forces arising from the material structure and other charged constituents. By choosing an extremely small test charge, the disturbance caused to the source distribution becomes negligible. This ensures that the electric field remains a property of the original charge distribution and can be defined consistently. Therefore, the stability of the source charges is maintained through internal binding forces within the material. Hence Option C is correct.

The force acting on a test charge depends on both the charge magnitude and its position. Therefore, 1 → c. The ratio F/q is independent of the test charge and defines the electric field. Hence, 2 → d. Electric field exists throughout three-dimensional space surrounding source charges. Thus, 3 → a. For a single point charge, the electric field depends only on radial distance and possesses spherical symmetry. Therefore, 4 → b. The correct correspondence is: 1-c, 2-d, 3-a, 4-b. This matching follows directly from the NCERT definition of electric field and point-charge field distributions.

For a positive point charge placed at the center of a spherical surface, the electric field at every point on the sphere is directed radially outward. The outward normal vector to a spherical surface is also directed radially outward from the center. Therefore, the electric field vector and the outward normal vector are parallel at every point on the sphere. Hence, and This gives the maximum value of electric flux through the surface element. Thus Option C is correct.

For a negative point charge, electric field lines are directed radially inward toward the charge. Therefore Statement 1 is correct. For a spherical Gaussian surface surrounding the negative charge, the outward area vector points away from the center while the electric field points toward the center. Hence the angle between them is: making Statement 3 correct. According to Gauss's law, Since the enclosed charge is negative, the total electric flux is negative. Therefore Statement 2 is correct. The total flux depends only on the enclosed charge and not on the radius of the Gaussian surface. Hence Statement 4 is incorrect. Therefore Statements 1, 2 and 3 are correct.

The principle of superposition states that the force exerted by one charge on another remains unaffected by the presence of additional charges. Hence Statement 1 is correct. The net force on a charge is obtained by taking the vector sum of all individual Coulomb forces acting on it. Therefore Statement 2 is correct. Since electrostatic force is a vector quantity, the resultant force is determined using vector addition rules such as the parallelogram law. Thus Statement 3 is correct. Electrostatic forces obey the same vector addition principles as other mechanical forces. Therefore Statement 4 is incorrect. Hence Statements 1, 2 and 3 are correct.

For a point charge Q, Coulomb's law gives: Thus the electric field decreases as . For a short electric dipole at large distances , and Hence dipole fields vary as . Therefore the correct comparison is: Point charge → Dipole → Hence Option A is correct.

The electric force on both particles has magnitude: Acceleration is: Therefore, Substituting values: Thus the electron accelerates approximately 1833 times more than the proton. Unit verification: The ratio is dimensionless since masses cancel. Hence Option A is correct.

The concept of electromagnetic fields resolves the problem of action at a distance. Changes produced by a source charge do not affect distant charges instantaneously. Instead, information propagates through electromagnetic fields at the speed of light. These fields are not merely mathematical tools. They possess independent dynamics and evolve according to their own physical laws. Electromagnetic waves generated by accelerating charges continue propagating even after leaving the source region. This explains the finite time delay observed between cause and effect in electromagnetic interactions. Therefore, the modern field concept regards electromagnetic fields as real physical entities with independent evolution. Hence Option C is correct.

In three-dimensional geometry, the solid angle subtended by a small surface element ΔS placed perpendicular to the radius vector at a distance r is defined as: This concept is important in understanding electric field lines and flux distributions. For a point charge, field lines spread uniformly in all directions. The number of field lines crossing a given solid angle remains constant. Since the area of a sphere increases as , the density of field lines decreases as . The solid-angle concept provides a mathematical explanation for the inverse-square dependence of the electric field. Therefore, the correct relation is: Hence Option B is correct.

Faraday introduced field lines as a visual method to represent electric fields. A field line is defined as a curve drawn such that the tangent at every point gives the direction of the electric field at that point. If a positive test charge is placed on the field line, it tends to move in the direction indicated by the tangent. Thus, field lines provide information about the direction of the electric field throughout space. The density of field lines indicates field strength, while the tangent indicates field direction. Therefore, the defining property of a field line is that its tangent is parallel to the electric field vector at each point. Hence Option C is correct.

The number of field lines crossing a unit area is proportional to the electric field magnitude. Therefore 1 → c. The solid angle subtended by a small surface element is: Hence 2 → d. Faraday introduced the term "lines of force." Modern physics considers this expression somewhat misleading because fields are not literal physical strings. Thus 3 → b. The closeness or density of field lines indicates the relative strength of the electric field. Regions with crowded field lines correspond to stronger electric fields. Therefore 4 → a. Hence the correct matching is: 1-c, 2-d, 3-b, 4-a.

Electrostatic field lines possess several important properties. They originate from positive charges and terminate on negative charges. In regions free of charge, they continue smoothly without breaks. Unlike magnetic field lines, electrostatic field lines do not form closed loops. This follows from the conservative nature of electrostatic fields. Since the work done around a closed path is zero, electrostatic field lines cannot circulate continuously in closed curves. Magnetic field lines form closed loops because isolated magnetic charges do not exist. Electrostatic field lines behave differently because positive and negative charges act as sources and sinks. Therefore Statement B is incorrect. Hence Option B is correct.

An electric dipole placed in a uniform electric field experiences equal and opposite forces on its charges. These forces cancel, producing zero net force. Therefore Statement 1 is correct. Although the net force is zero, the forces form a couple and produce a torque. The magnitude of the torque is: Hence Statement 3 is correct. This torque tends to rotate the dipole so that its dipole moment vector becomes aligned with the electric field. Therefore Statement 4 is correct. Statement 2 is incorrect because the torque acting on a dipole in a uniform field is independent of the choice of origin. Hence Statements 1, 3 and 4 are correct.

In a non-uniform electric field, the forces acting on the positive and negative charges of a dipole are unequal because the field strength varies from one point to another. Consequently, a net force acts on the dipole. When the dipole moment vector p is parallel to the electric field, the positive charge experiences a stronger force in the region of stronger field than the negative charge experiences in the weaker region. Therefore, the dipole moves toward the region of increasing electric field strength. When the dipole moment vector is antiparallel to the field, the resultant force acts toward the region of decreasing field strength. Unlike a uniform electric field where only torque may act, a non-uniform field can produce both force and torque. Hence Option B is correct.

The electric field on the axis of a dipole is directed along the dipole moment vector, which points from the negative charge to the positive charge. Hence Statement 1 is correct. The electric field of a dipole is obtained by vector addition of the fields produced by +q and −q individually. Therefore Statement 3 is correct. For large distances: Since the dependence is , the field decreases faster than the dependence of a point charge. Thus Statement 4 is correct. Statement 2 is incorrect because the axial field contains the factor , not p alone. Hence Option D is correct.

For a dipole consisting of charges +q and −q separated by distance 2a, the electric field at a point on the axial line is obtained by superposing the fields due to both charges. The exact result is: where This expression remains valid for all axial distances except at the charge locations. When , leading to which is the approximate far-field formula. Hence Option B is correct.

Given: Dipole moment: Equatorial field: Unit verification: Hence Option D is correct.

At distances much larger than the dipole separation, the detailed values of q and a do not appear independently in the electric field expression. Instead, the field depends on the combination: which is called the electric dipole moment. For example: and Both expressions involve only the dipole moment p. Thus the distant field depends on the product of charge and separation, not on them individually. Hence Option C is correct.