electric potential

Physics Notes: Electric Potential

1. Potential Energy (PE)

• Potential energy is the energy an object has because of its position.

• In an electric field, a test charge has electric potential energy that depends on:

  • its charge ((q))

  • its position in the electric field.

Change in Potential Energy

[
\Delta PE = PE_b - PE_a
]

Where:

• (PE_a) = potential energy at point A

• (PE_b) = potential energy at point B

2. Electric Field Does Work

A charge placed in an electric field experiences a force:

[
F=qE
]

If the charge moves:

• With the electric field

  • Electric field does the work.

  • Potential energy decreases.

  • Kinetic energy increases.

• Against the electric field

  • You must do work on the charge.

  • Potential energy increases.

3. Work Done

For a charge moving a distance (d) in a uniform electric field:

[
W=-Eqd
]

Where:

• (W) = work (J)

• (E) = electric field (N/C)

• (q) = charge (C)

• (d) = distance (m)

The negative sign means moving with the field lowers potential energy.

4. Relationship Between Work and Potential Energy

If kinetic energy stays constant,

[
\Delta PE=W
]

Therefore,

[
\Delta PE=-Eqd
]

or

[
PE_b-PE_a=-Eqd
]

5. Electric Potential (Voltage)

Electric potential is the potential energy per unit charge.

[
V=\frac{PE}{q}
]

Where:

• (V) = electric potential (volts)

• (PE) = potential energy (joules)

• (q) = charge (coulombs)

Units

[
1\text{ volt}=1\frac{\text{joule}}{\text{coulomb}}
]

6. Electric Potential Difference

Potential difference (voltage) is

[
\Delta V=\frac{\Delta PE}{q}
]

Since

[
\Delta PE=W
]

then

[
\Delta V=\frac{W}{q}
]

Substituting (W=-Eqd),

[
\Delta V=-Ed
]

Magnitude only:

[
|\Delta V|=Ed
]

7. Important Relationships

Electric Force

[
F=qE
]

Electric Field

[
E=\frac{F}{q}
]

Electric Potential

[
V=\frac{PE}{q}
]

Potential Difference

[
\Delta V=\frac{\Delta PE}{q}
]

Work

[
W=-Eqd
]

Change in Potential Energy

[
\Delta PE=W=-Eqd
]

8. Positive vs Negative Charges

Positive Charge (+)

Naturally moves

• from high voltage

• to low voltage

Result:

• Potential energy decreases.

Negative Charge (−)

Naturally moves

• from low voltage

• to high voltage

Result:

• Potential energy decreases.

9. Parallel Plates

Between parallel plates:

• Electric field is uniform.

• Equipotential lines are perpendicular to the electric field.

• Higher charge density creates a stronger electric field.

Relationship:

[
\Delta V=Ed
]

Increasing either:

• electric field ((E))

• distance ((d))

increases the voltage difference.

10. Lightning

Clouds become polarized.

• Top of cloud → mostly positive

• Bottom of cloud → mostly negative

• Ground becomes positively charged.

When the electric field becomes strong enough, electrons rapidly move from the cloud to the ground.

This produces lightning.

11. Millikan Oil Drop Experiment

Purpose:

• Measured the charge of one electron.

Setup:

• Two parallel plates.

• Tiny charged oil drops placed between them.

• Voltage adjusted until an oil drop stayed suspended.

When suspended,

Electric force = Weight

[
F_E=F_G
]

or

[
qE=mg
]

Millikan discovered that every oil drop's charge was a whole-number multiple of

[
1.60\times10^{-19}\text{ C}
]

This is the charge of one electron.

12. Conservation of Energy

Energy cannot be created or destroyed.

It can only be:

• transferred

• converted from one form to another

In an electric field:

Potential Energy ↓ → Kinetic Energy ↑

Potential Energy ↑ → External Work Required

Total energy remains constant.

Formula Sheet

Exam Tips

• Positive charge: moves from high voltage → low voltage.

• Negative charge: moves from low voltage → high voltage.

• Moving with the electric field lowers potential energy.

• Moving against the electric field increases potential energy.

• Electric potential (V) is energy per unit charge.

• Voltage is measured in volts (J/C).

• The electric field between parallel plates is uniform.

• Remember these core equations:

  • (F=qE)

  • (E=\frac{F}{q})

  • (W=-Eqd)

  • (V=\frac{PE}{q})

  • (\Delta V=-Ed)