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Electric Charge (DP IB Physics)

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Ann Howell

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DP Physics: SLDP Physics: HL

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

Examiner Tips and Tricks

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 qA = −8.0 µC, qB = −2.0 µC, qC = +5.0 µC, and qD = +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 subscript f i n a l end subscript space equals space fraction numerator Q subscript 1 space plus space Q subscript 2 over denominator 2 end fraction

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 qB = −2.0 µC and qD = +12.0 µC

Q subscript f i n a l end subscript space equals space fraction numerator 12.0 space minus space 2.0 over denominator 2 end fraction space equals space plus 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 subscript f i n a l end subscript space equals space fraction numerator Q subscript 1 space plus space Q subscript 2 space plus space Q subscript 3 space plus space Q subscript 4 over denominator 4 end fraction

Step 2: Determine the charge on each sphere

  • The average charge on each sphere is

Q subscript f i n a l end subscript space equals space fraction numerator 12.0 space plus space 5.0 space minus space 2.0 space minus space 8.0 over denominator 4 end fraction space equals plus 1.75 μC

Note: you would also get the same result if you used qB = qD = +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 space o f space e l e c t r o n s space equals space fraction numerator c h a r g e space o n space s p h e r e over denominator e end fraction

Step 2: Determine the number of electrons required

n u m b e r space o f space e l e c t r o n s space equals space fraction numerator 1.75 cross times 10 to the power of negative 6 end exponent over denominator 1.60 cross times 10 to the power of negative 19 end exponent end fraction space equals space 1.094 cross times 10 to the power of 13

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

Examiner Tips and Tricks

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

straight n space rightwards arrow space straight p to the power of plus space plus space straight e to the power of minus space plus space straight nu with bar on top subscript straight e

charge on LHS = 0

charge on RHS = 1 + (−1) + 0 = 0

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    Ann Howell

    Author: Ann Howell

    Expertise: Physics Content Creator

    Ann obtained her Maths and Physics degree from the University of Bath before completing her PGCE in Science and Maths teaching. She spent ten years teaching Maths and Physics to wonderful students from all around the world whilst living in China, Ethiopia and Nepal. Now based in beautiful Devon she is thrilled to be creating awesome Physics resources to make Physics more accessible and understandable for all students, no matter their schooling or background.