Electric fields

The mathematical analogy helps with graphs, superposition and energy changes, but the signs must be reconsidered rather than copied. Electric potential can be positive or negative relative to infinity depending on the source charge, whereas the potential of an isolated positive mass is negative. A negative test charge feels force opposite to electric field direction, while a positive test charge follows it. Field strengths are vectors that add by components; potentials are scalars that add algebraically. A point with zero field need not have zero potential in either type of combined-field problem.

The voltage in the plate formula is a potential difference between two positions, whereas V = kQ/r gives potential at one point relative to infinity. Mixing them can accidentally produce the wrong distance dependence. Near plate edges, field lines bend and the field is no longer uniform, so the simple plate expression is an approximation. Outside a spherically symmetric charge distribution the point-charge result can be used with distance from its centre. Inside an extended distribution, the same total-charge formula is not automatically valid; the distribution and conductor conditions matter.

The field produces constant acceleration qE/m along its direction for a positive charge and opposite to it for a negative charge. A perpendicular velocity component stays constant if no other force acts. The shared time links these motions just as in projectile calculations, but the electric acceleration depends on the charge-to-mass ratio and can reverse with charge sign. After the particle leaves the field, the electric force from that ideal region is no longer applied. The subsequent path follows its exit velocity until another force acts; do not keep curving it indefinitely.

At the midpoint between two equal positive charges, each field points away from its source. The two fields have equal magnitude and opposite directions, so their resultant is zero. Both potentials are positive, however, and add to a positive total. Between equal opposite charges, the midpoint gives the reverse contrast: potentials cancel, while fields point in the same direction and reinforce. The zero of potential is a chosen reference, while zero field has the physical meaning of no net electric force on a small test charge at that point.

Field direction is defined using a positive test charge, so the electron’s force is opposite to the field arrow. The energy equation keeps the signs consistent: ΔU = qΔV and the work done by the field is −ΔU. A positive ΔV combined with negative q gives a potential-energy decrease. Do not interpret the phrase higher voltage as universally meaning higher potential energy for every particle. If the electron starts with a velocity against its force, it may slow before reversing, so the direction of instantaneous motion need not immediately match the direction of acceleration.

For a point charge, equipotential surfaces are concentric spheres and the field is radial. Between ideal parallel plates, equipotentials are parallel planes and the field crosses them normally. Closer spacing between equally stepped potential surfaces indicates a stronger field because the potential changes more rapidly with distance. A charged particle is not required to travel along a field line or remain on an equipotential; its trajectory also depends on its initial velocity. Use field arrows to determine acceleration, not as a drawing of every possible path through the region.