Electric charge and its basic properties
Charge is a basic property of matter. It is additive, conserved and quantised: every charge is a whole-number multiple of e.
What is electric charge?
Electric charge is a basic property of matter, like mass. It comes in two kinds, named positive and negative by Benjamin Franklin. Like charges repel and unlike charges attract. When you rub a glass rod with silk, electrons move from the glass to the silk. The rod becomes positive and the silk becomes equally negative. A plastic rod rubbed with fur becomes negative. Rubbing never creates charge: it only transfers electrons from one body to another. A gold-leaf electroscope detects charge: its leaves spread apart when charge reaches them.
Three basic properties of charge
| Property | What it means | Example |
|---|---|---|
| Additivity | Charge is a scalar. The total charge of a system is the algebraic sum of all the charges in it. | +2 C, +5 C and −3 C together give +4 C. |
| Conservation | The total charge of an isolated system never changes. Charge can be transferred, but not created or destroyed. | Rubbing gives +q to the glass and −q to the silk: the total stays zero. When a neutron decays into a proton, an electron and a neutral antineutrino, the total charge stays zero. |
| Quantisation | Every free charge is a whole-number multiple of the basic charge e: q = ne, where n = 0, ±1, ±2, ... | No body can carry a charge of 1.5e. |
Conductors vs insulators
A metal spoon rubbed while held in the hand does not stay charged: the charge leaks through your body to the ground, as both are conductors. A metal rod held by a plastic handle, and rubbed without touching the metal, does get charged.
Why we do not notice quantisation
- The basic charge e = 1.6 × 10⁻¹⁹ C is extremely small.
- A charge of just 1 μC equals about 6.25 × 10¹² electronic charges.
- Adding or removing a few electrons changes such a charge by a tiny fraction, so charge seems continuous at large scale.
- At the scale of atoms and nuclei, quantisation matters and must be used.
Worked example: electrons transferred
A polythene strip rubbed with wool gains a charge of −3.2 × 10⁻⁷ C. (a) How many electrons were transferred, and in which direction? (b) Is there a transfer of mass? (Charge of an electron = 1.6 × 10⁻¹⁹ C, mass of an electron = 9.1 × 10⁻³¹ kg)
- Given: q = −3.2 × 10⁻⁷ C, e = 1.6 × 10⁻¹⁹ C.
- Formula: q = ne, so n = |q|/e.
- n = 3.2 × 10⁻⁷ C ÷ 1.6 × 10⁻¹⁹ C = 2 × 10¹².
- The strip is negative, so electrons moved from the wool to the polythene.
- (b) Mass moved = n × mass of one electron = 2 × 10¹² × 9.1 × 10⁻³¹ kg = 1.82 × 10⁻¹⁸ kg.
(a) 2 × 10¹² electrons, from the wool to the polythene; (b) yes, about 1.8 × 10⁻¹⁸ kg, far too small to measure
Worked example: is this charge possible?
Can a body carry a charge of (a) 4.8 × 10⁻¹⁸ C, (b) 2.4 × 10⁻¹⁹ C? (e = 1.6 × 10⁻¹⁹ C)
- Use q = ne: the charge is possible only if n is a whole number.
- (a) n = 4.8 × 10⁻¹⁸ ÷ 1.6 × 10⁻¹⁹ = 30, a whole number.
- (b) n = 2.4 × 10⁻¹⁹ ÷ 1.6 × 10⁻¹⁹ = 1.5, not a whole number.
(a) Possible (30 electronic charges); (b) not possible, because charge is quantised
Pulling off a woollen sweater in a dry Delhi winter gives tiny crackles and shocks, because rubbing moves electrons between you and the wool. Petrol tankers carry a metal chain or rope that touches the road, so that such charge leaks safely into the ground and cannot make a spark.
1 marks: “What is meant by quantisation of electric charge?” The charge on any body is a whole-number multiple of e: q = ne, with n = 0, ±1, ±2, ... and e = 1.6 × 10⁻¹⁹ C.
2 marks: “How many electrons must be removed from a neutral metal sphere to give it a charge of +8 μC?” n = q/e = 8 × 10⁻⁶ ÷ 1.6 × 10⁻¹⁹ = 5 × 10¹³ electrons. Removing electrons leaves the sphere positive.
2 marks: “State the law of conservation of charge. Give one example.” The total charge of an isolated system stays constant. Example: rubbing a glass rod with silk gives +q to the rod and −q to the silk, so the total stays zero.
Charge is ACQ: Additive (add with signs), Conserved (never made or lost), Quantised (q = ne).