Electromagnetism — fields and induction

Describe a field

A field assigns a physical quantity to positions in space and, when needed, time. Electric and magnetic fields have magnitude and direction. For a stationary test charge q, the electric force is q × E. For a moving charge, the full law also includes a magnetic contribution.

A vector is a quantity with direction as well as magnitude. Here we start with one line: choose right as the positive direction and left as negative. This keeps the arithmetic simple without pretending that real fields have only one dimension.

Follow the sign of a force

In an invented uniform electric field of +200 N/C, place a small positive test charge of +0.000002 C. Assume it does not disturb the source of the field.

force = charge × electric field
force = 0.000002 C × 200 N/C = +0.0004 N

Its force points right. Replacing it with a charge of the same magnitude and opposite sign reverses that force. A force specifies a push, not the object's current velocity; determining motion would also require its mass and initial conditions.

These values describe a prescribed field, not a method for constructing it.

Let a changing flux produce a voltage

Magnetic flux summarizes the magnetic field passing through an oriented surface. In a simple fixed loop, a changing flux produces an electromotive force, or emf, measured in volts. The induction reference gives the negative flux-change rate; the minus sign depends on the agreed loop and surface orientations.

For a fictional single-turn fixed loop, assume the signed flux increases uniformly from 0.001 Wb to 0.004 Wb in 0.003 s. Wb means weber, a unit equal to V × s.

flux change = 0.004 Wb - 0.001 Wb = 0.003 Wb
emf = -0.003 Wb / 0.003 s = -1 V

This calculation predicts an emf. It does not specify a current: that also depends on the connected circuit. A constant flux through this fixed loop gives zero induced emf from this mechanism.

Try it yourself

1. What is the electric force on +1 μC in a field of -300 N/C?
2. If a fixed loop's signed flux increases by 0.006 Wb in 0.003 s, what emf follows under the same orientation convention?
3. Does the emf alone determine the current?

Answers and limits

The force is -300 μN. The emf is -2 V. Current still requires a circuit model. These idealized exercises omit field geometry calculations, self-inductance and radiation; they do not describe a practical coil or transformer design.

Next: quantum basics.