Electric Field and Electric Field Lines

The governing relation is F = qE. The electric-field direction is defined as the force direction on a positive test charge, so the positive charge feels a force toward the east. For a negative charge, q is negative, so its force is opposite to E, toward the west. Because the charges have equal magnitude, |F| = |q|E is equal for both. Hence B is correct; A has the wrong direction and C reverses both directions.

Use superposition and resolve each field into components. Since both charges are positive, the field at the point points away from each charge. By symmetry, the horizontal component from the left charge is cancelled by the equal opposite horizontal component from the right charge. The vertical components point upward and add, so the resultant field is upward. Therefore A is correct; it is not zero because the vertical components do not cancel.

For a negative charge, the electric field at any point is directed toward the charge. At the point above the midpoint, the field from the left charge has a downward component and the field from the right charge also has a downward component. Their horizontal components are equal and opposite, so they cancel, while the downward components add. Thus option B is correct; the net field is not zero because the vertical components reinforce one another.

Step 1: Field due to a point charge is directly proportional to source charge and inversely proportional to square of distance. Step 2: Halving charge makes field half, while halving distance makes it four times. Step 3: Together the field becomes double.

Electric field and electric potential are related but are not the same quantity. The field is the negative spatial rate of change of potential, E = −dV/dr, whereas potential is the value of energy per unit charge. At a point where the potential has a stationary value, its slope and hence the field can be zero even when V is non-zero. Thus B is correct; A and C incorrectly identify field with potential, and D denies a well-defined physical quantity.

The electric force on a charge is F = qE. For a nonzero positive test charge, zero force requires E = 0 at that location. However, field-line density is conventionally used to represent relative field strength: closely spaced lines indicate a strong, nonzero field, not a zero field. Thus the two claims conflict when referring to the same point and same diagram. Option A is correct; B reverses the density rule, while C and D are unrelated or false.

Step 1: Between like charges, the two fields can be in opposite directions. Step 2: To balance the field of the larger charge, the point must be closer to the smaller charge. Step 3: For unequal like charges, zero field lies between them closer to the smaller charge.

For a dipole, the positive charge produces a field directed away from it, whereas the negative charge produces a field directed toward itself. At a point outside the positive charge on the axial line, these two contributions are opposite, but the point is closer to the positive charge. Since electric-field magnitude varies inversely with the square of distance, the positive-charge contribution is larger, so the net field is outward.

By definition, the dipole moment points from the negative charge to the positive charge. At an equatorial point, the fields due to the two charges have components perpendicular to the dipole axis that cancel. Their components along the axis add in the direction from the positive charge toward the negative charge. Consequently, the net electric field is opposite to the dipole-moment direction, not zero.

A field line is drawn so that its tangent at any point represents the direction of the electric-field vector. At a point where the net field is exactly zero, the vector has zero magnitude and no unique direction. Consequently, a field line cannot have a defined tangent there, so drawing one as passing exactly through that null point is physically misleading. The field is not strongest there; it is zero.

Step 1: The electric field of a point charge is directly proportional to charge and inversely proportional to square of distance. Step 2: Doubling charge makes field double and tripling distance makes it one ninth, so the net factor is two ninth. Step 3: In ratio questions, handle charge and distance changes separately.

The governing concept is superposition of vector electric fields. At the exact midpoint, the two equal positive charges produce fields of equal magnitude in opposite horizontal directions, so the resultant is zero. At a point shifted upward, symmetry makes the horizontal components cancel, but both vertical components point upward and add. Therefore option A is correct; the fields do not vanish, and positive charges repel rather than attract.

The governing idea is superposition together with the inverse-square law, E = kQ/r². Between two positive charges, the fields point in opposite directions, so cancellation requires equal magnitudes. Since the larger charge produces a stronger field at comparable distances, the balance point must be farther from it and nearer the smaller charge. It is therefore not generally the midpoint; options B, C and D contradict the field law.

The relevant concept is vector superposition. In the region between a positive and a negative charge, the field points away from the positive charge and toward the negative charge; both directions are the same along the joining line. Thus the magnitudes add rather than cancel, so the net field cannot be zero there. Options B, C and D are false because field lines exist and both signs of charge produce electric fields.

Step 1: In electrostatic equilibrium, free charges arrange so that field inside the conducting material is zero. Step 2: If there is no charge in the cavity, the field inside the cavity is also zero. Step 3: Do not assume direct penetration of outside field into an empty closed conductor cavity.

Electric field lines conventionally originate on positive charges and terminate on negative charges. At the midpoint between the two charges, the field due to the positive charge points away from it, and the field due to the negative charge points toward it; both point from positive to negative. Therefore the field direction at the centre is from + to −, along the dipole axis. The dipole moment itself points oppositely, from − to +.

The density of electric field lines represents relative field strength: closely packed lines indicate a strong field. A uniform field requires both constant direction and constant magnitude, conventionally shown by straight, parallel, equally spaced lines. If the arrow direction changes rapidly from place to place, the field direction varies spatially, so the field is non-uniform. Thus A combines both observations; B, C and D do not.

Parallel field lines indicate that the field direction remains the same throughout the displayed region. However, line spacing is also important: decreasing spacing means more lines cross the same area, representing increasing field magnitude. Therefore the field has a constant direction but a strength that increases along the diagram, so it is non-uniform. A uniform field would require parallel lines with equal spacing, making B incorrect.

Step 1: Electric field is produced by source charges and should not depend on the value of the test charge. Step 2: If test charge is halved, force is also halved, so force per charge remains the same. Step 3: A test charge measures the field; it should not define the source field.

The electric field points left, but a negative charge experiences force opposite to the field because F = qE with q < 0. Thus, its force is rightward. Field lines becoming sparse toward the left indicate that the field magnitude decreases in that direction. For a fixed charge, force magnitude |F| = |q|E also decreases. Therefore option A correctly identifies both direction and change in magnitude.

Electric field at a point is defined as the force per unit positive test charge produced by the original source-charge arrangement, with the test charge sufficiently small not to disturb it. If the test charge is large and moves the source charges, the source configuration changes. The measured force and calculated field then describe a different arrangement, not the original one. Thus option A identifies the principal error.

For a positive test charge, F = qE. If q is nonzero and the force is zero, the net electric field at that point is zero. This does not require every source charge to be absent: fields produced by several charges can have equal magnitudes and opposite directions, so their vector sum cancels. Therefore option A is correct. Zero net field must not be confused with zero individual fields or no nearby charges.

Step 1: The field of a point charge is directly proportional to charge and inversely proportional to the square of distance. Step 2: Tripling charge increases the field three times but tripling distance reduces it nine times. Step 3: The net effect is three divided by nine, so the field becomes one-third.

Step 1: For unequal like charges, the zero-field point lies between the charges. Step 2: To balance the stronger field of the larger charge, the point must be farther from the larger charge and closer to the smaller charge. Step 3: Hence it shifts towards the smaller charge.

Step 1: The midpoint is equally distant from both charges, so the magnitudes of the two fields are equal. Step 2: The positive charge gives a field away from itself, and the negative charge gives a field towards itself. Step 3: At the midpoint, both directions are from positive to negative, so the fields add.