PHYC10004 Chap.1 Electric Charge, Coulomb's Law and Electric Fields
Electric Charge, Coulomb's Law and Electric Fields
Week 1 of PHYC10004 starts with electric charge itself: two signs, conserved, carried by electrons and protons, free to move in conductors and fixed in insulators. Coulomb's law then gives the force between two point charges, an inverse-square attraction or repulsion along the line joining them, scaled by the permittivity of the space between them.
The chapter's main tool is superposition.
The force on a charge, or the field at a point, is the vector sum of the contributions from every other charge, so the working is a matter of drawing one arrow per source, resolving it into components and adding. The electric field, force per unit test charge, lets you describe the influence of a charge distribution without a test charge present, and field lines turn that field into a picture with three drawing rules.
The chapter closes with the electric dipole from Week 3, whose moment p = qd feels a torque but no net force in a uniform field.
What this chapter covers
- 01
Charge and Charge Conservation
- 02
Conductors and Insulators
- 03
Coulomb's Law and Permittivity
- 04
Superposition of Forces
- 05
The Electric Field
- 06
Field Line Rules
- 07
Fields of Continuous Charge
- 08
Electric Dipoles in a Field
Worked example · free
Locate the point where two like charges produce zero field
- 1Between two like charges the two fields point in opposite directions, so a zero can exist there; outside the pair both fields point the same way.
- 1Set the magnitudes equal at position x: k(9.0 nC)/x² = k(4.0 nC)/(0.50 − x)².
- 1Take square roots, keeping the positive root for a point between the charges: 3.0/x = 2.0/(0.50 − x), so 1.5 − 3.0x = 2.0x.
- 1Solve: x = 0.30 m, which is closer to the smaller charge, as it must be.
Key terms
- Coulomb's Law
- Coulomb's law gives the force between two point charges as the product of the charges divided by 4πε₀r², directed along the line joining them. Like charges repel and unlike charges attract.
- Permittivity
- Permittivity is the property of the medium between charges that sets the strength of the electric force. In vacuum it is ε₀ = 8.854 × 10⁻¹² C² N⁻¹ m⁻²; a material with dielectric constant κ has ε = κε₀.
- Superposition Principle
- The superposition principle states that the net force or field from several charges is the vector sum of the contributions each charge would produce alone.
- Electric Field
- The electric field at a point is the force per unit charge that a small positive test charge would experience there, measured in N/C or equivalently V/m.
- Field Line
- A field line is a curve whose tangent gives the field direction. Lines start on positive charge, end on negative charge, never cross, and are denser where the field is stronger.
- Dipole Moment
- The dipole moment of two equal and opposite charges is p = qd, a vector pointing from the negative to the positive charge.
Electric Charge, Coulomb's Law and Electric Fields FAQ
Why does a charged rod attract a neutral object?
The rod polarises the neutral object. Opposite charge is drawn to the near side and like charge pushed to the far side, so the attraction on the nearer charge is stronger than the repulsion on the farther charge. The net force is towards the rod, and in a perfectly uniform field there would be only a twist, not a pull.
When should I resolve vectors in an electrostatics problem?
Resolve whenever two or more forces or fields at one point are not along the same line. Find each magnitude from its own distance, use the angles in your diagram to split each arrow into x and y parts, add the parts, then give a magnitude with an angle measured from a named axis.
Does the field of a long charged rod fall off as one over r squared?
No. Near a long rod the field falls roughly as one over the distance, because the contributions from the length of the rod add up. Only when you are far from a short rod, compared with its length, does it behave like a point charge with an inverse-square field.
What rules should I state when sketching field lines?
State that lines begin on positive charge and end on negative charge or at infinity, that they never cross, that their density shows field strength, and that they meet a conductor's surface at right angles. Past papers ask for the sketch and the rules together, so give both.
Exam move
Practise Coulomb problems as diagrams first. For every arrangement, mark each source charge and draw an arrow for its push or pull before writing a single number, then label the angle you will use to resolve it. Work a set of problems that mix collinear charges, a right-angle triangle and a symmetric arrangement where one component cancels, and finish each with a magnitude and a direction.
Then rehearse the two short explanations that recur: why the force follows an inverse-square law, using flux spreading over a sphere, and why forces obey superposition and vector addition. Finally, sketch the dipole pattern from memory until the three drawing rules are automatic.
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