# CURRENT ELECTRICITY AND MAGNETISM (2)

1. The field produced by a straight current-carrying conductor

When a current flows through a conductor, it produces a magnetic field, shown in the above diagram as the green circular arrows surrounding the wire.

The direction of the current in the conductor is indicated by the symbols which indicates a current flowing away from you, or INTO the plane of the screen, and , which indicates a current moving towards you, or OUT of the screen ( do not be confused!)

The magnetic field is represented by lines of flux which are closer together in regions of higher field. A small permanent magnet suspended in the field would align tangentially to the flux lines at any point.

(The arrows which are shown in the diagrams of the flux lines above indicate the direction in which the north-seeking pole of such a magnet would point, i.e. from N to S).

If you imagine that the conductor is held in the right hand, with the thumb pointing in the direction of the current flow, then the fingers curl the direction of the magnetic field (This is the Right Hand Rule or the Palm Rule. See also Maxwell's corkscrew rule).

2. The force between parallel current-carrying conductors

If currents pass along two parallel wires, each wire will set up a magnetic field and the fields will interact according to the rules described in the previous topic.

Two parallel conductors which each carry a current in the SAME DIRECTION will ATTRACT one another, while two such conductors which carry currents in an OPPOSITE DIRECTION will REPEL each other: (Explanation)

We need to be able to calculate the force between two conductors carrying different currents.

Consider two wires which are at a distance d apart, parallel to one another for a length l, and carrying currents I1 and I2 respectively.

The force is proportional to the currents I1 and I2 and the length l, and inversely proportional to d.Thus

I1 and I2 are measured in ampere (A) (see a definition of the ampere and the coulomb), l and d are measured in metres (m) and F is measured in newton (N). k has the value of 2 x 10-7 N·A-2.

Why do parallel current-carrying conductors attract one another?

Conductor B produces a magnetic field which is perpendicular to the current flow in A.

The force acting on A will be at right angles to the current flow and at right angles to the magnetic field.

Now apply Fleming's left Hand rule: point the first finger in the direction of the field, the second finger in the direction of the current, and then your thumb will point in the direction of the direction of the force experienced by the conductor A.

A similar argument will show that the field due to conductor A will cause a force on B towards A. Hence the conductors are attracted to each other.

Definition of the ampere

Having established the relationship between the currents flowing in two parallel conductors and the force acting between them, it is possible to define the ampere in terms of other physical quantities:

Definition of the ampere
"The ampere is the constant current which, if maintained in two parallel conductors of infinite length, of negligible cross-section, and placed one metre apart in a vacuum, would produce between these conductors force of 2 x 10-7N per metre of length."
1. In the equation shown on the right, according to the above definition, l = d = 1 m. I1 = I2 = 1 A. k is chosen to be 2 x 10-7 N·A-2 in order to be consistent with the laws of electrolysis.
2. A vacuum is specified since certain media will attenuate the magnetic field. Errors of measurement in air are negligibly small.
3. Conductors of infinite length are specified to eliminate end-effects. The definition is modified to apply to coils of wire when accurate measurements are made in practice.

Definition of the coulomb

Since a current is nothing but a flow of charge, we can now measure charge, Q, in terms of the current, I, passing a cross-section of the conductor in time, t,

This enables us to define the coulomb:

Definition of the coulomb
"A coulomb is the quantity of charge passing a cross-section of conductor in one second when the current is one ampere."

FARADAY'S FIRST LAW may be stated as follows:

"The amount of any substance deposited, evolved, or dissolved at an electrode is directly proportional to the amount of electrical charge passing through the circuit."

FARADAY'S SECOND LAW may be stated as follows:

"The mass of different substances produced by the same quantity of electricity are directly proportional to the molar masses of the substances concerned, and inversely proportional to the number of electrons in the relevant half-reaction."

Maxwell's Corkscrew Rule

This rule predicts the direction of the magnetic field lines around a straight conductor through which a steady electric current is flowing.

Imagine that you are using a right-handed corkscrew in such a way that it points in the direction of the current flow. The direction of rotation of the handle then gives the direction of the magnetic field lines.

Current in and out: do not be confused!

It is easy to forget which of the symbols and refer to current "in" or "out". Consider a dart, with the current flowing in the direction of its point (above, left). Now stick it in a piece of cardboard, and view it from the top. It mimicks the current flowing away from the viewer and into the cardboard. See how the vanes appear (above, center). Now turn the cardboard over, and look at the point, which symbolises the current flowing towards the viewer. Only a dot is visible (above, right). You will never forget this!