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Electric fields

Electricity and magnetism · level 6, lesson 1 of 6

A question to start

A charged balloon pulls on your hair from several centimetres away. How does the push or pull get across the gap?

The idea

A charge sets up an electric field in the space around it. Any other charge placed in that field feels a force. The field strength is the force on each coulomb:

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

in newtons per coulomb (N/C), which is the same as volts per metre (V/m).

Field lines show the field. They point the way a positive charge would be pushed: away from + and towards −. Where the lines are closer together, the field is stronger.

Between two flat metal plates with a voltage \(V\) across a gap \(d\), the field is the same everywhere:

\[E = \frac{V}{d}.\]
+ + plate− plate: even field

Worked examples

1. The force. A charge of \(2 \times 10^{-6}\) C in a field of 5,000 N/C feels \(F = qE = 0.01\) N.

2. Two plates. 300 V across a gap of 2 cm: \(E = 300/0.02 = 15{,}000\) V/m.

3. A spark. Dry air near the ground on Earth breaks down at about 3,000,000 V/m. Across a 1 cm gap, that takes \(3\times10^6 \times 0.01 = 30{,}000\) V. Thin Mars air breaks down at only a few tens of thousands of V/m.

Try it

  1. A charge of \(5 \times 10^{-9}\) C feels a force of \(1.5 \times 10^{-4}\) N. Find the field.
  2. Find the field between plates 5 mm apart with 100 V across them.
  3. Which way do field lines point near a negative charge?
  4. Suppose Mars air breaks down at 30,000 V/m. What voltage would make a spark jump 1 cm?
Answers
  1. \(E = F/q = 30{,}000\) N/C.
  2. \(100/0.005 = 20{,}000\) V/m.
  3. Inwards, towards it.
  4. \(30{,}000 \times 0.01 = 300\) V.

Common mistake

"Field lines are paths that charges follow." They show the direction of the force at each point. A moving charge can cross field lines, the way a thrown ball does not follow the direction of gravity.

Where it leads