Field Strength from Potential | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

Field Strength from Potential

A potential–distance graph shows how electric potential changes as position changes.

If potential changes by a large amount over a short distance, the electric field is strong. This is why the graph's slope matters.

Read the slope before using the formula

Flat graph

Potential does not change with distance, so the field is zero.

Gentle slope

Potential changes slowly with distance, so the field is weak.

Steep slope

Potential changes quickly with distance, so the field is strong.

Field magnitude comes from how steep the graph is. Field direction is towards decreasing potential.

E=-\dfrac{\mathrm dV}{\mathrm dx}

Symbols

$E$ = electric field strength in the x-direction (V m⁻¹)
$\mathrm dV/\mathrm dx$ = gradient of the potential–distance graph (V m⁻¹)

The minus sign means the field points towards decreasing potential.
For a curve, draw a tangent at the point. Find its gradient, then change the sign.

Field equals potential gradient and the minus sign are separate marks (9702/41/O/N/24 Q5(a)).

Swipe left or right to see the whole diagram →

V–x between two charged conducting spheres. The exam skill is reading it backwards: flat sections give each sphere's radius (V is constant inside a conductor), the signs of V near each surface give the charge signs.

Read charge, radius and field from a potential graph

The flat part inside each conducting sphere shows constant potential and zero field.
The end of a flat part gives the sphere radius.
Positive potential near a sphere means positive charge. Negative potential means negative charge.
Equal-shaped parts of the graph can show equal charge magnitudes.

Recent graph questions award marks for the radii, charge signs and relative magnitudes (9702/42/M/J/24 Q5(b)).