Electric Charge

Charge is the property of matter responsible for the electric force
The unit of charge is the coulomb (C), where one coulomb is defined as:

The charge carried by an electric current of one ampere in one second

Charge is a scalar quantity

Quantisation of Charge

Matter is made up of atoms
- Electrons have a negative charge
- Protons have a positive charge
- Neutrons are neutral (no charge)

Carbon atom structure

The number of negative electrons in an atom balances the number of positive protons

Most everyday objects are neutral (zero charge) because they contain atoms with equal numbers of protons and electrons
- This is because protons and electrons both have a magnitude of charge equal to the elementary charge

An object can become charged when it obtains an excess of protons or electrons
- The quantity of charge will always equal a whole number of protons or electrons
- Therefore, charge is quantised

Direction of Electric Forces

When two charges are close together, they exert a force on each other, this could be:
- Attractive (the objects get closer together)
- Repulsive (the objects move further apart)

Attraction and Repulsion

Opposite charges attract, like charges repel

Whether two objects attract or repel depends on their charge
- If the charges are the opposite, they will attract
- If the charges are the same, they will repel

Attraction or Repulsion Summary Table

Exam Tip

Remember the saying: “Opposites attract”.

Conservation of Electric Charge

In the same way that energy must be conserved, charge must also be conserved
The law of conservation of charge states that

The total charge in an isolated system remains constant

This means that charge:
- can be transferred
- cannot be created or destroyed

In this context, an isolated system refers to the objects involved in the transfer of charge

Worked example

Four identical metal spheres have charges of q_A = −8.0 µC, q_B = −2.0 µC, q_C = +5.0 µC, and q_D = +12.0 µC.

(a)

Two of the spheres are brought into contact briefly, and then they are separated. Which spheres are they if the final charge on each one is +5.0 µC?

(b)

All four spheres are brought into contact briefly and then separated. What is the final charge on each sphere?

(c)

How many electrons would have to be added to one of the spheres in (b) to make it electrically neutral?

Answer:

(a)

Step 1: Apply the principle of conservation of charge to the scenario

When two charged spheres come into contact, the charges are shared between them until they are evenly distributed i.e. both spheres have the same charge
The charge on each sphere is equal to the average of the two charges

$Q_{f i n a l} = \frac{Q_{1} + Q_{2}}{2}$

Step 2: Determine the charge on each sphere

For the average charge to be +5 μC, the sum of the two charges must be +10 μC
This can only be achieved with charges q_B = −2.0 µC and q_D = +12.0 µC

$Q_{f i n a l} = \frac{12.0 - 2.0}{2} = + 5.0$ μC

(b)

Step 1: Apply the principle of conservation of charge to the scenario

The charge on each sphere is equal to the average of the four charges (i.e. the total charge is equally distributed between all four spheres)

$Q_{f i n a l} = \frac{Q_{1} + Q_{2} + Q_{3} + Q_{4}}{4}$

Step 2: Determine the charge on each sphere

The average charge on each sphere is

$Q_{f i n a l} = \frac{12.0 + 5.0 - 2.0 - 8.0}{4} = + 1.75$ μC

Note: you would also get the same result if you used q_B = q_D = +5.0 µC

(c)

Step 1: Recall the charge of an electron and that charge is quantised

Electrons have a charge of e = −1.60 × 10⁻¹⁹ C
Therefore, the number of electrons required is

$n u m b e r o f e l e c t r o n s = \frac{c h a r g e o n s p h e r e}{e}$

Step 2: Determine the number of electrons required

$n u m b e r o f e l e c t r o n s = \frac{1.75 \times 10^{- 6}}{1.60 \times 10^{- 19}} = 1.094 \times 10^{13}$

Therefore, 1.1 × 10¹³ electrons are required to neutralise one of the charges

Exam Tip

The law of conservation of charge is also important when considering systems of particles and processes, such as nuclear decay

For example, in beta decay, when a neutron decays into a proton, an electron must also be produced to balance the charges

$n \to p^{+} + e^{-} + {\bar{ν}}_{e}$

charge on LHS = 0

charge on RHS = 1 + (−1) + 0 = 0

Electric Charge (SL IB Physics)

Revision Note

Electric Charge

Quantisation of Charge

Direction of Electric Forces

Attraction or Repulsion Summary Table

Exam Tip

Conservation of Electric Charge

Worked example

Exam Tip

Author: Ann H