Learn/Electricity

Electricity · AP Physics 2 · 6 min

Electric field is not electric potential

Field tells force per charge; potential tells energy per charge. They are related, but not interchangeable.

01 The trap

Where the wrong model begins.

Wrong path

Students treat zero potential as zero field, or use volts and newtons per coulomb as if they measure the same thing.

Why it feels right

Both ideas describe an electric environment, and both get larger near charges in many simple examples.

02 Correct model

The first-principles repair.

model repair

Electric field points in the direction a positive test charge would accelerate. Electric potential is a scalar energy-per-charge map. Field is related to how potential changes with position.

01Ask whether the quantity needs direction.
02Add potentials as scalars; add fields as vectors.
03Use ΔU = q ΔV for energy changes.
04Use F = qE when the question asks for force or acceleration.

03 Mini-example

Same problem, cleaner model.

worked trap check

Prompt

At the midpoint between +q and -q, what are V and E?

Common wrong answer

Both are zero because the charges cancel.

Correct reasoning

V is zero by scalar cancellation, but E is nonzero because both field vectors point from + toward -.

Diagnostic cue

If equal positive and negative charges appear, pause: potential may cancel while field reinforces.

04 Guided practice

Try it before the solution.

Warm-up isolates the principle. Bridge changes the context. Contest-style requires a complete setup on less familiar geometry.

warm-upAP Physics 2

Midpoint between opposite charges

A +q charge and a -q charge are separated by distance 2a. At the midpoint, is electric potential zero, electric field zero, both, or neither?

Hint

At the midpoint, the field from +q points away from +q, and the field from -q points toward -q.

Solution

The potential is zero because kq/a + k(-q)/a = 0. The electric field is not zero because both field vectors point from the positive charge toward the negative charge.

Trap: Assuming cancellation works the same way for potential and field.

bridgeAP Physics 2

Energy from potential difference

A proton moves from point A to point B where V_B - V_A = -120 V. Find the change in electric potential energy.

Hint

A proton has charge +e.

Solution

ΔU = q ΔV = (+1.60e-19 C)(-120 V) = -1.92e-17 J. The proton's electric potential energy decreases.

Trap: Dropping the sign and reporting only a positive energy change.

contest-styleAP Physics 2

Equipotential motion

A charge moves along an equipotential curve in an electrostatic field. What is the work done by the electric force?

Hint

Electric work is -ΔU, and ΔU = q ΔV.

Solution

ΔV = 0, so ΔU = q ΔV = 0 and the electric force does zero net work along that path.

Trap: Thinking a force must do work whenever the charge moves.

bridgeAP Physics 2

Electron through a potential rise

An electron moves between two points with ΔV = +35 V. What is its change in electric potential energy?

Hint

Use q = -1.60 × 10⁻¹⁹ C.

Solution

ΔU = (-1.60 × 10⁻¹⁹ C)(+35 V) = -5.60 × 10⁻¹⁸ J.

Trap: Reporting a positive change because the potential increased.

05 Mock checks

When the drills feel clean.

AP Physics 245 min

Physics 2 mixed model check

A cross-unit check for the AP Physics 2 habit that matters most: choosing the right model before calculating.

9 questions · 27 pts

06 Keep learning

Forces

Electric field is not electric potential

Where the wrong model begins.

The first-principles repair.

Same problem, cleaner model.

Try it before the solution.

Midpoint between opposite charges

Energy from potential difference

Equipotential motion

Electron through a potential rise

When the drills feel clean.

Physics 2 mixed model check

Normal force is not always mg

Static friction is not always maximum

Constant speed does not mean zero acceleration