Electric fields
| English | Chinese | Pinyin |
|---|---|---|
| electric field | 电场 | diàn chǎng |
| electric field strength | 电场强度 | diàn chǎng qiáng dù |
| field line | 场线 | chǎng xiàn |
| test charge | 检验电荷 | jiǎn yàn diàn hè |
| vector | 矢量 | shǐliàng |
| negative charge | 负电荷 | fù diàn hè |
| point charge | 点电荷 | diǎn diàn hè |
| dipole | 偶极子 | ǒu jí zi |
| uniform field | 匀强场 | yún qiáng chǎng |
A force with nothing in between
- Rub a comb on your hair and hold it over torn paper. The paper jumps up to meet it, across a gap of air, with nothing touching.
- Newton called action at a distance across empty space philosophically unacceptable, and he was right to be uneasy. The modern answer is that the comb changes the space around it, and the paper responds to the space it is in.
- That altered region is an electric field 电场, and the whole of this topic is a way of describing it precisely enough to calculate with.
- This lesson is the definition of electric field strength 电场强度, the force it produces, and how field lines 场线 represent it.
Field strength
- The electric field strength at a point is the force per unit positive charge acting on a small test charge 检验电荷 placed at that point:
- Three words carry the two marks. Force per unit charge, not "force on a charge". Positive, which is what fixes the direction. And small or test, so the charge does not disturb the field it is measuring.
- The unit is $\text{N/C}$, which is the same as $\text{V/m}$. $E$ is a vector 矢量.
Electric field strength is the force per unit:
$E = \dfrac{F}{q}$ — the force on each coulomb of a small positive test charge.
A charge of $2.0\ \text{C}$ feels a force of $6.0\ \text{N}$. What is the field strength?
$E = \dfrac{F}{q} = \dfrac{6.0}{2.0} = 3.0\ \dfrac{\text{N}}{\text{C}}$.
Which words are needed in the two-mark definition of electric field strength? Select all that apply.
A moving charge feels the same electric force. The three marked ideas are per unit charge, positive, and a small test charge.
The force on a charge
- Rearranged, the field tells you the force on any charge placed in it:
- A positive charge is pushed along the field. A negative charge 负电荷 is pushed against it, since $q$ is negative.
- In these problems gravity is almost always negligible. An electron in a field of $1500\ \text{V/m}$ accelerates at $2.6 \times 10^{14}\ \text{m/s}^2$, against $9.81$ from gravity, so the weight is ignored unless the question is specifically about balancing it.
A field strong enough to tear electrons off air molecules
The force on a negative charge is opposite to the field direction.
Field direction is defined for a positive charge; a negative charge feels the opposite force.
Worked example: field from an acceleration
- A proton accelerates at $2.00\ \text{m/s}^2$ in an electric field, with no other force acting. Find the field strength. ($m_{\text{p}} = 1.67 \times 10^{-27}\ \text{kg}$, $e = 1.60 \times 10^{-19}\ \text{C}$.)
- The electric force is the only force, so $qE = ma$.
- Run the same rearrangement the other way for the acceleration of an electron in a given field: $a = eE/m_{\text{e}}$, which is enormous because the electron's mass is so small.
A proton (mass 1.67e-27 kg, charge 1.60e-19 C) accelerates at 2.00 m/s^2 in an electric field alone. What is the field strength, in units of 10^-8 V/m?
The electric force is the only force, so qE = ma and E = ma/q = 2.09e-8 V/m. The same rearrangement gives an electron's acceleration in a known field.
Field lines
- A field line shows, by its direction, the direction of the force on a positive charge placed there, and by its spacing, the strength of the field: closer lines mean a stronger field.
- Lines start on positive charges and end on negative ones, or run to infinity. They never cross, since the force at a point has one direction.
- Every line carries an arrow, and lines meet the surface of a conductor at right angles.
- A sketch is marked on exactly those points: arrows drawn, lines not crossing, correct starts and ends, and sensible spacing.
Four standard patterns worth being able to draw from memory
The patterns to know
- A positive point charge 点电荷: radial lines pointing outwards. A negative one: radial lines pointing inwards.
- Two opposite charges, a dipole 偶极子: lines curving from the positive to the negative.
- Two parallel charged plates: equally spaced parallel lines, a uniform field 匀强场, apart from the curvature at the edges.
Electric fields
E ∝ Q / r²
A charge sets up a radial field — out for +, in for −, obeying the inverse-square law.
Electric field lines:
They run from + to −, never cross, and are closer where the field is stronger.
Field lines drawn closer together mean a ____ field.
Line spacing shows the strength — closer lines, stronger field.
Which are true of electric field lines? Select all that apply.
A field line shows the direction of the force, not the trajectory: a charge entering sideways follows a curve that crosses the lines.
A charged conducting sphere
- Charge on an isolated conductor sits on its outer surface, spread evenly if the sphere is alone.
- Outside, the field lines are radial and evenly spaced: exactly the pattern of a point charge at the centre, so $r$ is measured from the centre.
- Inside a hollow or solid conductor the field is zero, and the conductor is therefore an equipotential.
- On an $E$ against $x$ graph for such a sphere, the radius is where $E$ jumps up from zero, and the charge follows from any point on the curve using $Q = 4\pi\varepsilon_0 r^2 E$.
Marks that slip away
- The definition is force per unit positive charge on a small test charge. All three ideas are marked.
- Field lines never cross and always carry an arrow. A sketch without arrows scores nothing.
- Inside a conductor the field is zero, and outside it behaves as a point charge at the centre.
- Gravity is negligible for a charged particle in a field unless the question is about balancing weight, as with an oil drop.
What is the electric field inside a hollow charged conducting sphere?
The fields of all the surface charges cancel inside, so the conductor is an equipotential. Outside it behaves as a point charge at the centre.
You've got it
- electric field strength is the force per unit positive charge on a small test charge: $E = F/q$, a vector in $\text{N/C}$ or $\text{V/m}$
- $F = qE$: positive charges are pushed along the field, negative ones against it, and gravity is normally negligible
- field lines show direction by their arrows and strength by their spacing; they start on positive, end on negative, never cross, and meet conductors at right angles
- a charged sphere behaves outside as a point charge at its centre, and the field inside a conductor is zero