Moving Charges and Magnetic Field

Lesson

Part 1 — currents make magnetic fields: how to define B, and how to calculate it for wires, coils and solenoids.

In this lesson you will

Describe Oersted’s observation and define the magnetic field B from the force F = q(v × B)
State the Biot–Savart law in vector form and use it to find the field at the centre and on the axis of a circular coil
Apply Ampere’s circuital law to a long straight wire and a long solenoid, and use the formula for a finite straight wire

Diagram

Oersted’s observation

In 1820 Hans Christian Oersted noticed that a compass needle placed near a wire deflected whenever a current flowed, and reversed its deflection when the current was reversed.

A current (moving charge) produces a magnetic field around it.
The field lines of a straight wire are circles round the wire (right-hand grip rule: thumb along I, fingers curl along B).
Electricity and magnetism are linked: the start of electromagnetism.

Concept

Defining the magnetic field B

A charge $q$ moving with velocity $\vec v$ through a magnetic field feels a force $\vec F = q\left(\vec v \times \vec B\right),\qquad F = qvB\sin\theta$ This defines $\vec B$ : its size is $B = \dfrac{F}{qv\sin\theta}$ , and $\vec F$ is perpendicular to both $\vec v$ and $\vec B$ .

SI unit: tesla (T): 1 T = 1 N A⁻¹ m⁻¹ = 1 N s C⁻¹ m⁻¹. The gauss, 1 G = 10⁻⁴ T, is also met.
No force if the charge is at rest or moves along $\vec B$ ; largest force, $qvB$ , when $\vec v \perp \vec B$ .

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