Magnetic Field due to Electric Current

Introduction — Electricity That Behaves Like a Magnet

A compass needle swings to point north; the speakers in your phone vibrate; an MRI machine peers inside your body. All of these depend on the same hidden link — a moving charge creates a magnetic field. This chapter explores that link, discovered almost by accident in 1820 by the Danish teacher Hans Christian Oersted, and then unravels how we tame it in electromagnets, motors and generators.

12.1 Magnet and Magnetic Field

A magnet is a piece of material that attracts iron, nickel and cobalt. Every bar magnet has two poles — a north-seeking pole (N) and a south-seeking pole (S). Like poles repel; unlike poles attract. If a bar magnet is cut into pieces, each piece is still a complete magnet with its own N and S — isolated monopoles do not exist in nature.

12.1.1 Magnetic Field Lines

To visualise a field that we cannot see, Michael Faraday introduced magnetic field lines. Their pattern is revealed by sprinkling iron filings around a bar magnet — each tiny filing turns into a miniature magnet and lines up along the field.

12.1.2 Oersted's Discovery (1820)

While passing current through a straight wire kept above a compass, Oersted noticed that the compass needle deflected. Reversing the current reversed the deflection. This single observation proved that an electric current produces a magnetic field around it — the very foundation of this chapter.

12.2 Magnetic Field Due to a Current-Carrying Straight Conductor

When iron filings are sprinkled on a cardboard pierced by a vertical current-carrying wire, the filings arrange themselves in concentric circles around the wire. The field lines therefore form circles whose plane is perpendicular to the wire and whose centres lie on the wire.

The strength of the field \(B\) at a point:

• is directly proportional to the current \(I\) through the conductor;
• is inversely proportional to the distance \(r\) from the wire, \(B \propto 1/r\).

12.2.1 Right-Hand Thumb Rule (Maxwell's Rule)

12.3 Magnetic Field Due to a Current Through a Circular Loop

A straight conductor is bent into a single loop. At every point on the loop, the right-hand rule is still valid — so on one side of the loop all the field lines come out of the plane, while on the other side they go in. Near the centre of the loop the many arcs add up to an almost straight field perpendicular to the plane of the loop.

The field at the centre depends on:

• Current \(I\) — more current, stronger field.
• Radius \(r\) — smaller loop, stronger field at centre.
• Number of turns \(n\) — if \(n\) identical turns are wound one over the other, the fields add up: \(B_\text{total} = n \times B_\text{one\ turn}\).

12.4 Magnetic Field Due to a Solenoid

A solenoid is a long coil of many closely wound turns of insulated copper wire wound in the shape of a cylinder. When current flows, each turn acts like a small loop. All the turns together give a pattern of field lines that is remarkable in three ways:

A strong field inside a solenoid can be used to magnetise a piece of magnetic material placed in it — this is how permanent magnets are made in industry.

12.5 Electromagnet — A Temporary Magnet

If a soft iron core is placed inside a solenoid, the iron core gets powerfully magnetised as long as the current flows. Switching off the current switches off the magnetism. Such a device is called an electromagnet.

Permanent magnet vs Electromagnet