078 – Static electricity

Static electricity is the oldest branch of the subject and still the one people meet first: a jumper crackling as it comes off, a door handle that stings after a walk across a carpet, hair standing away from a comb, cling film that will not let go of itself. Industrially the same effect has to be managed rather than admired — it is why fuel tankers are bonded to earth before filling, why electronic components ship in conductive bags, and it is also put to work deliberately in photocopiers, laser printers, electrostatic paint spraying and the precipitators that clean flue gases.

The physics behind all of it is one sentence long: when two different insulating materials are brought into intimate contact and separated, electrons move from one surface to the other, leaving one object with a net negative charge and the other with an equal positive charge. Which way the electrons go depends only on the pair of materials, and the materials can be ranked in a list — the triboelectric or electrostatic series — in which whichever member sits higher gives up electrons and becomes positive. Once charged, the objects obey Coulomb’s law: like charges repel, opposite charges attract, and the force falls off as the square of the separation.

In this laboratory you will suspend light balls from insulating stems so that they are free to swing, charge them by bringing wool or cotton to them, and then present the charged balls to one another two at a time. Polyethylene charged by wool, acetate charged by cotton, each material against its charging cloth and each against the other — six confrontations in all, recorded in a results table. From the pattern of attractions and repulsions you will work out the sign each material takes and reconstruct the part of the electrostatic series that governs these four substances.

Educational Goals

Charging an object and knowing that you have

• Charge a suspended insulator using a second material and describe, in terms of electrons, what has happened to both objects.
• Explain why the two objects necessarily carry equal and opposite charges, and why neither creates charge from nothing.

Reading attraction and repulsion correctly

• Predict the interaction of any two of the four materials once their positions in the electrostatic series are known.
• Recognise that repulsion proves two objects carry like charges, while attraction does not by itself prove anything, because a neutral object is also attracted to a charged one.

Using the electrostatic series

• Place polyethylene, acetate, wool and cotton in order from the experimental results rather than by looking the answer up.
• State that only the relative position of two materials matters, so that the same substance can be positive against one partner and negative against another.

Applying Coulomb’s law

• Write F = kq₁q₂/r² and use it to explain why the balls interact strongly at two centimetres and not at all at twenty.
• Estimate the size of the charge involved from the deflection of a suspended ball, and compare it with the number of atoms on the ball’s surface.

Observing and documenting systematically

• Complete a results table in which every pairing is recorded, including the ones that were expected to be uninteresting.
• Repeat a trial that fails, and give a physical reason why a charged ball loses its charge over time.

Protocol

1. Hang a clamp at the top of each universal stand, as high as possible.
2. Suspend a rigid movable rod on each clamp.
3. Hang a teal polyethylene ball on each rigid stem.

Transfer of static electricity between a wool ball and a polyethylene ball

1. Take the gray wool ball and bring it close to the teal polyethylene ball suspended from the rod of the left stand. Wait a few seconds for the teal polyethylene ball to become charged with static electricity (it will be attracted to the gray wool ball).
2. Then bring the gray wool ball close to the second teal polyethylene ball on the right. Wait a few seconds for the teal polyethylene ball to become charged with static electricity (it will be attracted to the gray wool ball).

Reaction between two polyethylene balls charged with static electricity

1. Unhook the teal polyethylene ball on the left and, without letting the two balls touch, bring this ball close to the one suspended on the right. The observations are recorded in the results table. Then wait until the balls no longer interact with each other.

Note : If the reaction between the balls does not work, restart the steps for loading the balls with the wool ball.

Transfer of static electricity between a cotton ball and an acetate ball.

1. Place the teal polyethylene ball on the table and take the green cotton ball, then gently bring it close to the suspended teal polyethylene ball on the right. Wait a few seconds for the teal polyethylene ball to become charged with static electricity (it will be attracted to the green cotton ball).
2. Hang a pink acetate ball on the rigid stem on the left.
3. Take the green cotton ball and gently bring it close to the pink acetate ball suspended on the left. Wait a few seconds for the pink acetate ball to become charged with static electricity (it will be attracted to the green cotton ball).

Reaction between an acetate ball and a polyethylene ball charged with static electricity

1. Detach the pink acetate ball and, without the two balls touching each other, bring this ball close to the teal polyethylene ball suspended on the right. The observations are recorded in the results table. Then wait until the balls no longer interact with each other.

Transfer of static electricity between a cotton ball and acetate balls

1. Rehang the pink acetate ball on the left.
2. Unhook and place back on the table the teal polyethylene ball on the right.
3. Hang the second pink acetate ball on the rigid stem available on the right.
4. Take the green cotton ball and gently bring it close to the pink acetate ball suspended on the left. Wait a few seconds for the pink acetate ball to become charged with static electricity (it will be attracted to the green cotton ball).
5. Take the same green cotton ball and gently bring it close to the pink acetate ball suspended on the right. Wait a few seconds for the pink acetate ball to become charged with static electricity (it will be attracted to the green cotton ball).

Reaction between two acetate balls charged with static electricity

1. Detach the pink acetate ball on the left and, without letting the two balls touch, bring this ball close to the one suspended on the right. The observations are recorded in the results table. Then wait until the balls no longer interact with each other.

Note : If the reaction between the balls does not work, repeat the previous steps to properly load the balls.

2. Unhook and place the pink acetate balls, the stems and the clamps.

Anticipated Outcomes

How the balls are charged. In a physical version of this experiment charge is transferred by contact and friction: the wool has to be rubbed against the polyethylene, and charge does not cross an air gap. This simulation abbreviates that step — bringing the wool or cotton ball close to a suspended ball is enough to load it. Everything after the loading behaves exactly as charged objects do, so the results table below is the one a real bench would produce; only the charging gesture is simplified.

What each material does. Polyethylene charged against wool takes electrons and becomes negative, leaving the wool positive. Polyethylene charged against cotton likewise becomes negative and leaves the cotton positive. Acetate charged against cotton gives up electrons and becomes positive, leaving the cotton negative. Cotton therefore appears with both signs in this laboratory, which is not a contradiction but the central lesson of the electrostatic series: a material has no charge of its own, only a position relative to its partner.

Why repulsion is the only proof. Four of the six rows are attractions and two are repulsions, and the two are worth more than the four. A charged object attracts a neutral one: its field pulls the neutral body’s own charges slightly apart, drawing the opposite sign nearer and pushing the like sign away, and because the Coulomb force falls with distance the nearer, opposite charge wins. That is why a charged rod picks up scraps of uncharged paper, and it means an attraction between two balls is consistent with three different situations — opposite charges, or one charged and one neutral, in either arrangement. Repulsion has no such loophole: two objects can only push each other apart if both are charged and both carry the same sign. A student asked to prove that the two polyethylene balls are negative must point at the repulsion, not at the attraction to the wool.

How much charge is involved. Coulomb’s law gives the force between two point charges as F = kq₁q₂/r², with k = 8.99 × 10⁹ N·m²/C². A suspended ball hangs at an angle when pushed sideways, and the geometry of a pendulum gives F = mg tan θ. Taking a light ball of about 1 g and a clearly visible deflection of 10°, the sideways force is F = 0.001 × 9.81 × tan 10° = 1.7 × 10⁻³ N. If the two balls carry equal charges q and sit 3 cm apart, then q = √(Fr²/k) = √((1.7 × 10⁻³ × 9 × 10⁻⁴)/(8.99 × 10⁹)) ≈ 1.3 × 10⁻⁸ C, that is about 13 nC. Divided by the electronic charge, 1.6 × 10⁻¹⁹ C, this is roughly 8 × 10¹⁰ electrons — an enormous-sounding number that is nevertheless about one electron for every ten thousand billion atoms on the ball’s surface. Static electricity is a very small imbalance made visible by a very strong force.

Why distance matters so much. The inverse square in Coulomb’s law is steep. The 1.7 × 10⁻³ N calculated at 3 cm becomes a quarter of that at 6 cm and a hundredth at 30 cm, by which point it is a thousand times smaller than the ball’s weight and nothing visible happens. This is the reason the protocol insists that the balls be brought close without touching, and the reason the effect appears so suddenly as the gap closes. It is also why touching must be avoided: on contact the two balls share their charge, and two objects carrying the same sign then repel from a standing start with much less charge each.

Why the charge does not last. The protocol tells you to wait until the balls stop interacting, and to recharge them if a trial fails. Both instructions have the same cause: charge leaks away, mainly along a microscopic film of water adsorbed on every surface, and the leak rate depends strongly on the humidity of the room. In dry winter air a charged insulator can hold its charge for many minutes; at 70 % relative humidity it may be gone in seconds. This is why static shocks are a winter phenomenon in temperate climates, and why a physical version of this laboratory works far better on a dry day. Touching a ball with a bare hand discharges it at once, the human body being a good enough conductor to carry a nanocoulomb to earth.

Honest limits of this experiment. Nothing here is measured: every result is a yes-or-no observation of attraction or repulsion, so no number in the paragraphs above can be checked against the laboratory as it stands. The charge estimate depends on a ball mass and a deflection angle that are assumed rather than read, and it treats two spheres a couple of centimetres apart as point charges, which flatters the arithmetic by perhaps tens of per cent. The simulation also charges by proximity rather than by rubbing, so the mechanism the electrostatic series describes — intimate contact and separation — is asserted on the page rather than demonstrated in the headset, and no humidity or leakage rate is modelled explicitly. A class that wants a measurement can get one cheaply: fix one ball, vary the separation, and record the deflection angle at each distance. Plotting tan θ against 1/r² should give a straight line through the origin, and that single graph turns a demonstration into an experiment.

Summary of Assignment by Grade Range

Grade 9–10

Focus. Observing charged objects and recording what they do.

Activities. Carry out all six pairings of the protocol and complete the results table. Predict, before each pairing, whether the balls will attract or repel, and count how many predictions were right.

Expected of the student. State the rule that like charges repel and opposite charges attract; say that charging moves electrons from one object to the other and does not create them; name which of the four materials ends up negative; and give two examples of static electricity outside the laboratory.

Grade 11

Focus. The electrostatic series as a predictive tool.

Activities. Deduce the order of the four materials from the results table without consulting a reference, then check it against a published series. Use the deduced order to predict the outcome of a pairing the protocol never performs, such as wool presented to a cotton-charged acetate ball.

Expected of the student. Explain why cotton takes opposite signs in two different rows of the table without any contradiction; write down which object gains electrons in each transfer and which loses them; state Coulomb’s law and use it to explain why the balls interact at two centimetres and not at twenty.

Grade 12 / College Level

Focus. Quantitative electrostatics and the logic of the evidence.

Activities. Estimate the charge on a ball from a pendulum deflection and Coulomb’s law, and convert it to a number of electrons and to a fraction of the surface atoms. Analyse polarisation and explain why an attraction is ambiguous evidence while a repulsion is not. Design the added measurement — deflection against separation — that would test the inverse-square law, and say what would have to be controlled for it to work.

Expected of the student. Derive F = mg tan θ for a suspended ball; justify or criticise the point-charge approximation at these separations; account for charge leakage in terms of surface conduction and humidity; and identify which of the six rows in the results table would survive if one ball were neutral rather than charged.

Laboratory essentials

Instruments

• Universal lab stands (2)
• Clamps (2)
• Rigid movable rods, one per stand, with insulating hooks

Products

• Polyethylene balls, teal (2)
• Acetate balls, pink (2)
• Wool ball, grey (1)
• Cotton ball, green (1)