Concept of Magnetic Field and Oersted's Experiment

A magnetic field, denoted $\vec{B}$, is the region of space surrounding a magnet or a

current-carrying conductor in which a magnetic pole, a small compass needle, a moving charge, or

another current-carrying conductor experiences a magnetic force or torque. Like the electric field

$\vec{E}$ of electrostatics, it is a vector field, having a magnitude and a direction at every

point in space, and its SI unit is the tesla ($\text{T}$), with a smaller, still commonly used

unit the gauss ($1\ \text{G} = 10^{-4}\ \text{T}$).

The crucial difference in source. An electrostatic field $\vec{E}$ is produced by charge simply

sitting still -- a charge at rest is enough. A magnetic field $\vec{B}$, by contrast, is produced

ONLY by a charge that is MOVING -- a charge at rest produces no magnetic field whatsoever. In

practice, the most common macroscopic source of a magnetic field is an electric current, since a

current is nothing but a very large number of charges all moving together through a conductor. This

is the single fact that separates the study of magnetism from the study of electrostatics, and is

the key idea Oersted's experiment revealed for the first time.

Oersted's experiment (1820). For roughly two centuries before 1820, electricity and magnetism

were studied as two entirely separate branches of physics, with no known connection between them.

Hans Christian Oersted, while demonstrating to his students that an electric current heats a wire,

noticed by chance that a small magnetic compass needle placed near the current-carrying wire was

deflected from its usual north-south orientation whenever the circuit was switched on, and returned

to pointing north-south the moment the current was switched off.

The key observations. Careful follow-up experimentation established three central facts. First,

the compass needle deflects only when current actually flows in the wire -- a stationary charge on

the same wire (before the switch is closed) produces no deflection at all. Second, the DIRECTION of

the deflection reverses when the direction of the current in the wire is reversed -- showing the

effect has a definite sense, not just a magnitude. Third, the needle always settles pointing roughly

TANGENT to an imaginary circle drawn around the wire, in a plane perpendicular to the wire -- showing

the magnetic field of a straight current-carrying wire forms closed circular loops encircling the

wire, in contrast to the straight radial field lines of a point charge.

The right-hand thumb rule. The direction of this circular field can be remembered with a simple

rule: if the wire is grasped in the right hand with the thumb pointing along the direction of

conventional current flow, the curled fingers point in the direction of the magnetic field lines

circling the wire. This rule recurs constantly through the rest of the chapter, in the Biot-Savart …