Electric Flux and Electric Dipole

Electric dipole moment is defined as p = qd, where q is the magnitude of charge and d is the separation vector between the effective positive and negative charge centres. In a polar molecule these centres do not coincide, producing a nonzero permanent dipole moment. Therefore option A is correct. A molecule need not have a net charge; equal total positive and negative charge can still be spatially separated.

A permanent dipole moment requires a lasting separation between the effective centres of positive and negative charge. In a non-polar molecule, the charge distribution is symmetric, so these centres generally coincide and the separation vector d is zero. From p = qd, the permanent dipole moment is therefore zero, making option A correct. Temporary induced dipoles may occur, but they do not represent a permanent dipole.

Studying electric flux develops the ability to interpret how an electric field passes through a surface, while studying a dipole explains the field produced by two equal and opposite charges separated by a distance. Together, these ideas connect field behaviour with geometry and charge arrangement. Hence option A is correct. The other options describe colour, temperature, or mass, none of which is the central purpose of these electrostatic concepts.

Electric flux represents the amount of electric field passing through a specified surface. For a uniform field and a plane surface, it is expressed as Φ = EA cos θ, where E is field strength, A is area, and θ is the angle between the field and the area vector. Hence option A gives the correct simple meaning. Current concerns charge flow in a conductor, while mass and colour are unrelated properties.

Electric flux is treated as a scalar quantity because its value is obtained from the dot product Φ = E · A = EA cos θ. A dot product produces a scalar, although its value can be positive, negative, or zero depending on orientation. Therefore option A is correct. It is not a vector merely because electric field and area are vectors, and it is not always zero; zero occurs only for particular orientations or field conditions.

Electric flux is given by Φ = EA cos θ. Since cos θ has no unit, the unit of flux is the unit of electric field multiplied by the unit of area. Electric field has unit N/C and area has unit m², so Φ has unit N·m²/C. Thus option A is correct. N/C alone is the unit of electric field, whereas the other two options do not result from multiplying field by area.

An area vector represents both the magnitude of a surface area and its orientation. By convention, for a plane surface its direction is along the normal, meaning perpendicular to the surface. Therefore option A is correct. The vector is not parallel to the surface, and it is not always downward or rightward; those directions depend on how the surface is placed and which normal is chosen. In flux calculations, the angle is measured from this normal.

For a plane surface, flux is Φ = EA cos θ, where θ is measured between the electric field and the area vector, which is normal to the surface. If the electric field is perpendicular to the surface, it is parallel or antiparallel to the area vector; for the usual outward direction, θ = 0° and cos θ = 1. Thus the magnitude of flux is maximum, so option A is correct. Zero flux occurs when the field is parallel to the surface.

Electric flux through a plane surface is Φ = EA cos θ, with θ measured between the electric field and the area vector. The area vector is perpendicular to the surface. When the electric field is parallel to the surface, it is perpendicular to the area vector, so θ = 90° and cos 90° = 0. Therefore the flux is zero, making option A correct. Maximum flux occurs when the field is normal to the surface, not parallel to it.

For a uniform electric field through a plane surface, flux is Φ = EA cos θ. Consequently, it depends on the field magnitude E, the surface area A, and the angle θ between the field and the area vector. Option A lists all three governing factors. The colour or mass of the surface does not enter the formula, and time alone does not determine flux in this electrostatic context. The angle must be measured from the normal, not from the surface itself.

For a uniform field, flux through a plane surface is Φ = EA cos θ. If the two surfaces have the same area and are in the same field, E and A are fixed, so the flux depends on θ. A smaller angle between the electric field and the area vector gives a larger value of cos θ and therefore greater flux. Hence option A is correct. Colour, mass, and thickness do not determine flux in this idealized relation.

An electric dipole is a system of two point charges having equal magnitudes and opposite signs, separated by a small finite distance. Thus, +q and −q together form a dipole, whereas two like charges or one isolated charge do not satisfy the definition. The separation is important because it gives the system a dipole moment, even though its total charge is zero. Therefore, option A is correct.

Electric dipole moment is defined as p = qd, where d is the displacement vector directed from the negative charge to the positive charge. Consequently, its direction is not necessarily upward, nor is it always opposite to an external electric field. Option B reverses the conventional definition and points from positive to negative. Hence option A is the unambiguous correct answer.

The magnitude of electric dipole moment is p = qd, where q is the magnitude of either charge and d is the separation between the charges. Charge has SI unit coulomb (C), while separation has SI unit metre (m). Multiplying them gives C m, or coulomb metre. N/C is the unit of electric field, and N m is torque or work, so option A is correct.

Electric dipole moment is a vector because it has both a definite magnitude and a definite direction. Its magnitude is p = qd, and its conventional direction is from the negative charge toward the positive charge. Although the net charge of a dipole is zero, its dipole moment need not be zero. Therefore, it is not scalar or always zero, making option A correct.

For a dipole, the magnitude of dipole moment is p = qd, where q is the charge magnitude and d is the fixed separation. If d remains unchanged and q is increased, their product increases in the same proportion. The direction, defined from negative to positive charge, does not disappear merely because the magnitude changes. Hence option A is correct.

The dipole moment is given by p = qd. Let the original value be p = qd. When the charge q stays constant and the separation changes from d to 2d, the new moment is p′ = q(2d) = 2qd = 2p. Thus the dipole moment becomes twice its original value. It does not become half, zero, or one-fourth, so option A is correct.

An ideal electric dipole contains charges +q and −q of equal magnitude. Adding them algebraically gives Qnet = (+q) + (−q) = 0. This zero net charge does not mean that the dipole has no electric field, because the charges are separated in space. Positive, negative, or infinite net charge would contradict the dipole definition. Therefore, option A is correct.

Net charge is a scalar algebraic sum, so +q and −q cancel when calculated together. Electric field, however, is a vector produced at each point by the individual charges. Since the positive and negative charges occupy different positions, their field vectors generally do not cancel everywhere; complete cancellation occurs only at particular locations or limits. Thus option A gives the correct reason.

The axial line of an electric dipole is the straight line passing through the centres of both charges. It contains the dipole axis and is directed along the line joining −q and +q. A line through the midpoint perpendicular to this axis is called the equatorial line, not the axial line. Circular or surface-related descriptions do not define dipole geometry. Hence option A is correct.

The equatorial line is the line that passes through the midpoint of the separation between the two dipole charges and is perpendicular to the dipole axis. Option B describes the axial line, which joins the charges. The last two choices refer vaguely to field-line directions and do not define a geometrical line of the dipole. Therefore, option A is correct.

The governing idea is the electric field of a short dipole on its axial line. At a far axial point, the fields due to the positive and negative charges combine in the direction of the dipole moment p, which is defined from negative charge to positive charge. Therefore option A is correct. Option B describes the far equatorial direction, while options C and D are incorrect for a nonzero dipole.

For a short electric dipole, the equatorial line is perpendicular to the dipole axis. At a distant point on this line, the transverse components of the two charge fields cancel, while their components along the axis combine opposite to p. Hence option A is correct. The field is not always zero, and option B is the axial-line result, not the equatorial one.

For a short dipole at distance r, the far axial field has magnitude E_axial = (1/4πε₀)(2p/r³), whereas the equatorial field has magnitude E_equatorial = (1/4πε₀)(p/r³). Dividing the first expression by the second gives E_axial/E_equatorial = 2. Thus option A is correct; it is neither equal nor half.

The far electric field of a short dipole follows E ∝ p/r³, where p is the dipole moment and r is the distance from its centre. Thus, if the distance is doubled, the field becomes 1/8 of its former value. Option A is correct. The inverse-square law belongs to an isolated point charge, not to the leading far field of a dipole.