Electric potential and field patternsEdexcel International A Level Physics: Revision notes
Section 1
Electric potential and field strength
The electric potential V at a point is the work done per unit positive charge in bringing a small test charge from infinity to that point. It is a scalar, measured in volts (J C⁻¹). The work done moving a charge Q through a potential difference ΔV is W = QΔV.
Field strength and potential are linked: the field strength is the negative of the potential gradient, E = −ΔV/Δx (or −dV/dx). The field points in the direction in which the potential falls most steeply.
E can be written in V m⁻¹ or N C⁻¹. They are equivalent.
Section 2
Uniform fields between parallel plates
Between two parallel plates with potential difference V and separation d, the field is uniform and
E = V/d
The field lines are parallel, equally spaced and perpendicular to the plates, and the potential changes uniformly with distance. The force on a charge Q is F = EQ = QV/d, the same everywhere between the plates.
Worked example: 600 V across plates 4.0 cm apart gives E = 600 ÷ 0.040 = 1.5 × 10⁴ V m⁻¹.
Convert the separation to metres before using E = V/d.
Section 3
Potential of a point charge
For a point charge Q (or a charged sphere, outside it) the potential at distance r is
V = Q/(4πε0r)
V is positive for a positive charge and negative for a negative charge, and it falls with 1/r. The field strength E = Q/(4πε0r²) falls with 1/r², and is the magnitude of the gradient of the V–r graph.
The work done by an external force moving a charge q between two points is W = qΔV. Moving a positive charge towards a positive source increases its potential energy.
Potential goes as 1/r but field strength goes as 1/r². Do not mix them up.
Section 4
Field lines and equipotentials
Field lines show the direction of the force on a positive charge, and are closest together where the field is strongest. An equipotential is a line or surface of constant potential.
- Equipotentials always cross field lines at right angles.
- No work is done moving a charge along an equipotential.
- Radial field: lines straight and radial, equipotentials concentric circles (spheres) that get further apart with distance.
- Uniform field: parallel, equally spaced lines, with equally spaced parallel equipotentials.
Must know
- E = −ΔV/Δx; in a uniform field E = V/d
- V = Q/(4πε0r) for a point charge (scalar, ∝ 1/r)
- W = QΔV for moving a charge through a p.d.
- Equipotentials cross field lines at right angles
- Radial and uniform field patterns, and their equipotentials
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Electric potential and field patterns
- Two large, flat, parallel metal plates are 4.0 cm apart in a vacuum. A potential difference of 600 V is maintained between them, with the upper plate positive.A proton is placed in the field between the plates. Calculate the force on the proton and state its direction. (Charge of a proton = 1.60 × 10⁻¹⁹ C.)2 marks
- An isolated small sphere carries a charge of +8.0 nC in a vacuum. Its charge may be treated as a point charge at its centre.Calculate the work done by an external force in moving a +2.0 nC charge slowly from 0.40 m to 0.20 m from the centre of the sphere.2 marks
- Along a straight line in a region of electric field, the potential falls uniformly from 240 V at a point X to 80 V at a point Y. The distance XY is 0.040 m.Calculate the electric field strength between X and Y, assuming it is uniform, and state its direction.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).