Electric Field and Electric Field Lines

The governing idea is symmetry of the charge distribution. For a very large uniformly charged plate, every point in the plane is equivalent, so sideways electric-field components produced by symmetric charge elements cancel. The remaining field must point perpendicular, or normal, to the plate. Its direction is away from a positive plate and toward a negative plate. Colour, mass, and temperature do not determine this ideal electrostatic direction.

Metals have a lattice of positive ion cores and a large number of conduction electrons that are not tied to one particular atom. When an electric field is applied, these mobile electrons acquire a small drift velocity, producing current and transporting negative charge. Protons and neutrons remain confined within nuclei, and the nuclei are fixed in the lattice. Thus option A is correct; the other choices confuse conduction electrons with nuclear particles.

An equipotential surface has the same electric potential at every point, so moving a test charge along it requires no work. Since E = −∇V, the electric field points in the direction of greatest decrease of potential and is normal to a constant-potential surface. Therefore field lines meet equipotential surfaces perpendicularly. They are not generally parallel or unrelated, so A is correct.

For an electrostatic field, field lines originate at positive charges and terminate at negative charges or at infinity. The field is conservative, with ∮E·dl = 0 around any closed path, so its lines do not circulate as closed loops. Magnetic field lines, in contrast, form closed loops. Option A gives the relevant source-to-sink picture and is correct.

This result follows from the superposition principle, which says that the net electric field is the vector sum of the fields produced by individual charges. At the midpoint, the distances from the two equal positive charges are identical, so each field has the same magnitude, E = kQ/r². The field from the left charge points right and that from the right charge points left. These equal opposite vectors cancel, giving zero net field. Positive charges do produce fields, so the other claims are incorrect.

For a point charge, the electric-field magnitude is E = k|Q|/r², so it follows an inverse-square relationship with distance. Let the original field be E₀ at distance r. When the distance becomes 3r, the new field is E' = k|Q|/(3r)² = k|Q|/(9r²) = E₀/9. Thus the field becomes one ninth of its initial value. One third would incorrectly use an inverse-first-power relation, while three and nine times have the wrong trend.

The electric field of a point charge is E = k|Q|/r². If Q changes to 2Q, the numerator makes the field twice as large. If r changes to 2r, the denominator becomes (2r)² = 4r², reducing the field by a factor of four. Therefore E' = k(2Q)/(2r)² = 2E/4 = E/2. The field is half the original value, not double or four times; it does not remain unchanged because both factors must be included.

An electric field is a vector field, and at any particular point its resultant vector has one definite direction. Field lines are drawn so that their tangent at a point represents this direction. If two field lines crossed, their tangents at the intersection would indicate two different electric-field directions at the same point, which is impossible for a single resultant field. Therefore field lines do not intersect. This fact is unrelated to units, and the lines are a meaningful visual model rather than decoration.

In electrostatic equilibrium, free charges inside a conductor are at rest and the electric field inside the conducting material is zero. If the conductor’s surface had a tangential component of electric field, free charges would experience a force along the surface and continue moving. They redistribute until the tangential component becomes zero. The remaining electric field at the surface is therefore normal, or perpendicular, to it. The field is not large inside, and conductors can carry charge on their surfaces.

Electric field-line diagrams use line direction to represent the field direction and line density to represent relative magnitude. Parallel lines indicate that the direction is essentially unchanged, but progressively smaller spacing means more lines cross each equal area. Therefore the field magnitude increases from one region to the next and the field is non-uniform. Hence B is correct; uniform fields require constant spacing, while C and D contradict the diagram.

The governing relation is F = qE. For a positive charge, q is positive, so the electric force has the same direction as the electric field. Newton’s second law, a = F/m, then gives acceleration along the field. In a uniform field the force and acceleration remain constant if no other force is considered, so the charge starts speeding up in that direction. Therefore A is correct; B reverses the direction and C and D ignore the electric force.

For a charge in an electric field, the force is F = qE. A negative charge has q < 0, so its force vector points opposite to the electric-field vector. Since acceleration follows the net force through a = F/m, its initial acceleration is also opposite to the field. Uniformity fixes the field direction but does not reverse this charge-sign rule. Thus B is correct; A applies to a positive charge, while C and D have no general basis.

At a fixed point, the electric field is the same for both test charges, and force is given by F = qE. If the second charge has the same magnitude but opposite sign, its force magnitude is |q|E, equal to the first force, while its direction reverses. A force east on the positive charge therefore becomes a force west on the equal negative charge. Hence B is correct; the magnitude is not doubled or zero.

For a point charge, the electric-field magnitude is E = k|Q|/r². At the same distance, increasing |Q| increases E, so a field-line diagram represents the stronger field with more lines or greater line density. Because the charge remains positive, the lines still point radially outward; increasing magnitude does not change their direction or make closed loops. Therefore A is correct, whereas B, C, and D contradict field-line conventions.

By definition, the tangent drawn to an electric field line at any point gives the direction of the electric field at that point. This is especially useful when the line is curved, because the field direction may vary from location to location. The tangent does not directly provide the exact source charge, temperature, or time. Therefore A is correct; line spacing, rather than the tangent alone, is used to indicate relative field strength.

The electric field is defined as the force per unit positive test charge, expressed as E = F/q for q > 0. Consequently, a positive charge experiences an electric force in the same direction as the field. Since the field at the point is directed east, the force on the placed positive charge is eastward. Therefore B is correct; west would apply to a negative charge, while north and south are unsupported by the given information.

The electric force is given by the vector equation F = qE. For a negative charge, q is negative, so multiplying the field vector by q reverses its direction. A westward electric field therefore produces an eastward force on the negative charge. Hence B is correct. Option A would be correct for a positive charge in the same field, while north and south do not follow from the stated field direction.

Electrostatic fields are conservative, so the line integral around any closed path is zero: ∮E·dl = 0. Their field lines begin on positive charge and terminate on negative charge, or extend to infinity; they do not continuously close on themselves. A diagram of closed circular electric-field lines would imply a non-conservative circulation pattern and is therefore incorrect for an electrostatic field. Closed loops are associated with magnetic field lines, so A is correct.

The governing concept is that the density or spacing of electric field lines represents the field magnitude, while the tangent to a line gives its direction. A uniform field must have both constant magnitude and constant direction. Here the direction remains the same, but changing spacing indicates changing magnitude. Therefore the field is non-uniform, so option B is correct. Option A ignores the magnitude change; C and D are unrelated.

The governing property of an isolated point charge is spherical symmetry. At every location around a positive point charge, the electric field is directed along the radius away from the charge; its magnitude depends only on distance, E = kQ/r². Thus the outward, symmetric pattern demonstrates a radially outward field, making option A correct. The other choices contradict the existence, symmetry, or direction of the field.

The governing rule is that the tangent to an electric field line at any point gives the unique electric-field direction there. If two field lines intersected, their tangents at the intersection would assign two different directions to the same point, which is impossible for a well-defined field. Thus the diagram is incorrect and option A is correct. The rule applies to positive, negative, and conductor-related field diagrams alike.

Electric field lines point in the direction of the electric field, and their equal spacing indicates a uniform magnitude in this region. The force on a charge is given by F = qE. Since the charge is positive, q is positive, so the force has the same direction as the electric field. The lines point from right to left; therefore option A is correct. Options B and C reverse or change the indicated direction, while option D is wrong because a nonzero field produces force on a nonzero charge.

The direction of electric field is shown by the field lines, so here E points from right to left. The force is F = qE. For a negative charge, q is negative, which reverses the force direction relative to the field. Hence the force points from left to right, making option B correct. Option A would apply to a positive charge, while C has no basis in the stated field and D is false because the field and charge are nonzero.

Electric field lines originate outward from positive charges. For two like positive charges, the field produced by each charge points away from that charge. In the region between them, the two field contributions oppose one another along the line joining the charges; the resulting pattern bends away from the central region rather than connecting the charges. Thus option A gives the correct physical reason. Options B and C contradict electrostatic behavior, and D reverses the rule because lines terminate on negative charges.

An equipotential surface has the same electric potential at every point, so moving a test charge along it requires no work. The electric field is related to potential by E = −∇V; consequently, it points in the direction of greatest decrease of potential and has no tangential component along an equipotential surface. Therefore field lines meet equipotential surfaces at right angles, making option A correct. The other choices contradict this fundamental electrostatic relation.