a region of space where a charge experiences a force.
Electric field strength (E)
the force per unit positive charge acting on a small stationary charge placed at that point.
Field line
a line showing the direction of the force on a small positive test charge at each point.
Key points
E is a vector; its direction is that of the force on a positive charge.
Field lines start on positive charges and end on negative charges.
Closer lines mean a stronger field; field lines never cross.
A negative charge feels a force opposite to the field direction.
Unit of E: N C-1, equivalent to V m-1.
Radial fields: lines point away from a positive charge and towards a negative one.
Equal and opposite charges: lines curve from + to -; the field is strongest where the lines crowd together.
Watch out!
Field lines show the force on a positive charge; an electron is pushed the other way.
Define E as force per unit positive charge; omitting "positive" loses the mark.
18.2Uniform electric fields
Definitions
Uniform field
a field in which the field strength is the same in magnitude and direction at every point.
Key points
Between parallel plates the field is uniform: parallel, equally spaced lines from + to -.
E = ΔV / Δd: field strength equals the potential gradient (magnitude).
The field bulges near the plate edges (non-uniform there).
A charge in a uniform field feels a constant force qE, so constant acceleration qE/m.
Charge entering at right angles to the field: constant velocity along the plates, uniform acceleration across them, so a parabolic path.
Charge moving along the field lines: it speeds up or slows down in a straight line; energy gained = qV.
Parallel plates: uniform field in the middle (equal spacing), bulging at the edges.
An electron entering the field is pushed towards the + plate and follows a parabola, like a projectile.
Watch out!
d is the plate separation in metres, not the plate length.
In a uniform field the force is the same everywhere between the plates, unlike a radial field.
18.3Electric force between point charges
Definitions
Coulomb's law
the electric force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation.
Point charge
a charge whose size is negligible compared with the distances involved; outside a charged conducting sphere, its charge acts as a point charge at the centre.
Key points
Like charges repel, unlike charges attract; the forces on the two charges are equal and opposite (Newton's third law).
Inverse-square law: doubling r gives one quarter of the force.
For spheres, r is measured centre to centre.
Same form as Newton's law of gravitation, but electric forces can repel and are far stronger.
A positive F from the formula means repulsion; a negative F means attraction.
Two like charges repel with equal and opposite forces; r is measured between centres.
F against r: an inverse-square curve; doubling r quarters F.
Watch out!
Square the separation: F ∝ 1/r2, not 1/r.
Convert distances to metres and charges to coulombs (1 μC = 10-6 C) before substituting.
18.4Electric field of a point charge
Definitions
Radial field
a field whose lines spread out from (or converge on) a point, with strength decreasing with distance.
Key points
Field of an isolated point charge is radial and obeys an inverse-square law.
Mirrors gravity (g = GM/r2) but can point outwards (+Q) or inwards (-Q).
Charged conducting sphere: E = 0 inside; outside, it acts as a point charge at its centre.
Field from several charges: add the individual field strengths as vectors.
Neutral point: where the fields of two charges cancel (between like charges, closer to the smaller one).
Charged conducting sphere of radius R: zero field inside, E ∝ 1/r2 outside.
Moving from r to 2r from a point charge, the field strength falls to one quarter.
Watch out!
E ∝ 1/r2 but V ∝ 1/r: doubling r quarters E but only halves V.
Adding fields from two charges: take account of direction, not just magnitude.
18.5Electric potential
Definitions
Electric potential (V)
the work done per unit positive charge in bringing a small test charge from infinity to that point.
Electric potential energy
the work done in bringing a charge from infinity to that point.
Equipotential
a surface on which every point has the same potential; no work is done moving a charge along it.
Key points
Potential is zero at infinity; V is a scalar, so potentials from several charges simply add.
Near a positive charge V is positive; near a negative charge V is negative.
Field strength = negative potential gradient: E = -dV/dr (field points towards falling potential).
On a V-r graph, E at a point = minus the gradient of the tangent.
Equipotentials are always perpendicular to field lines; for a point charge they are concentric spheres.
Work done moving charge q through a potential difference ΔV is W = qΔV.
V against r: positive for +Q, negative for -Q, both tending to zero at infinity; E = minus the tangent gradient.
Equipotentials (dashed circles) around a point charge are perpendicular to the radial field lines.
Watch out!
Electric potential can be positive or negative (gravitational potential is always negative): keep the sign of Q.
Potential is a scalar: add potentials from several charges algebraically, not as vectors.