The electric field at a point is the force per unit charge on a small positive test charge placed there. A charge produces a field in the space around it, and the field exerts a force F = qE on any charge q.
Coulomb’s law gives the force between two charges directly. The field description splits this into two steps.
Step one: a charge, called the source charge, produces an electric field at every point in the space around it. Step two: a charge placed at a point experiences a force determined by the field at that point.
The source charge produces the field whether or not another charge is present to experience a force.
Place a small positive test charge q₀ at a point and measure the force F on it. The electric field E at that point is:
E = F / q₀
E is a vector. Its direction is the direction of the force on a positive test charge. Its SI unit is the newton per coulomb (N/C).
For a single point charge Q, Coulomb’s law gives F = kQq₀/r². Dividing by q₀:
E = kQ / r²
The field points away from Q if Q is positive, and towards Q if Q is negative. It does not depend on q₀, because q₀ cancels. The field is a property of the source and the position.
The field at a point is E. How do you find the force on a charge q placed there?
Rearrange E = F/q:
F = qE
A charge of 3 C in a field of 10 N/C experiences a force of 30 N. A charge of −3 C at the same point experiences a force of 30 N in the opposite direction to E, because q is negative.
It separates the source from the charge acted on. The field of an arrangement of charges is calculated once. Then the force on any charge placed anywhere is F = qE.
Fields obey superposition. The field at a point due to several source charges is the vector sum of the fields due to each one. This follows from the superposition of forces.
The field is a physical quantity in its own right. This is shown by experiment, not by the definition. An electric field stores energy. When a source charge moves, the change in its field travels outwards at the speed of light, not instantly. Electromagnetic waves, including light, are changing electric and magnetic fields travelling through empty space. For charges at rest, the field description and Coulomb’s law give identical forces.
The definition uses a small test charge. Why must it be small?
The test charge also exerts forces on the source charges. If the sources are free to move, a large test charge would move them, and the field being measured would change.
Making q₀ very small makes these forces on the sources negligible. Strictly, the field is defined as the limit of F/q₀ as q₀ tends to zero.
A thermometer is designed on the same principle. It should have so little heat capacity that it does not noticeably change the temperature of what it measures.
1The electric field at a point is defined as…
2If the field at a point is E and a charge q is placed there, the force on it is F = ____.
3The direction of the electric field at a point is…
4A charge of 3 C is at a point where the field is 10 N/C. The force on it is…
5Why is the field description useful for many source charges?
6Why must the test charge used to measure the field be very small?
Next: field lines, and the flux of a field through a surface.
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