# Magnetic effect of electric current

A magnetic field is generated around an electric current in a conductive material, this phenomenon is called the magnetic effect of electric current.

## The Experiment of Oerested’s:

To confirm the magnetic effect of the electric current, Oersted did the following experiment:

Oersted installed a copper current-carrying circuit near a compass needle freely placed as per the following figure.

They found that as the current flows in the circuit the compass needle deflects when the direction of the current in the circuit is reversed, the direction of the deflection also changes. This proves that a current flowing in an electric conductor generates a magnetic field around it.

The direction of this magnetic field is determined by Ampere’s law of floating.

### Ampere’s Swimming Rule

According to this rule, if a person is swimming in the direction of current flowing in an electric conductor in such a way that his mouth is towards the north pole of the compass needle, then the north pole of the compass needle will rotate towards his left hand when the current in the conductor. Changing the direction of the electric current will also change the direction of deflection in the compass needle. This is the magnetic effect of electric current.

## Magnetic Field Due to a Current-Carrying Conductor: Bio-Severt’s Law

Bio and Severt based their experiments to find the formula for finding the intensity of magnetic field generated by a current-carrying wire which is as follows-

Let XY of a current-carrying conductor in which the electric current (I) is flowing through a small section of conductor wire(dl) at a distance r from the midpoint A of dl making an Î¸ angle from the direction of the current at the point P, the intensity of the magnetic field B low depends on things

1- It is directly proportional to the current flowing in the conductor

orÂ Â Â Â Â Â B Î± I

2- It is directly proportional to the length of the conductor segment

orÂ Â Â Â Â Â B Î± dl

3- It is inversely proportional to the square of the distance from the conductor segment to the point

orÂ Â Â Â Â B Î±1 /r^{2}

4- It is directly proportional to the angle of sine formed between the conductor segment and the point P

orÂ Â Â Â Â B Î± sinÎ¸

By mixing these four rules together

B Î± I dl sinÎ¸ /r^{2}

Hence, **intensity of magnetic fieldÂ B = Î¼0 / 4Ï€ Ã— I dl sinÎ¸ / r2 Newton / Ampere-meter**

This formula is called the Bio-Savert’s Rule.

Where Î¼_{0}/ 4Ï€ is a constant whose value is 10^{-7} Newton/Ampere^{2}

Î¼0 is called the permeability of a vacuum. Its value is 4Ï€ Ã—10^{-7 }Newton/Ampere^{2}.

### The Magnetic Field due to a Current-Carrying-Straight Conductor of Infinite length

We know that an electric current in a current-carrying wire produces a magnetic field around it. When an electric current of 1 Ampere flows in a straight wire of infinite length, the magnetic field generated at r distance from it is B depends on-

1- The magnetic field is directly proportional to the current flowing in the wireÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â orÂ Â Â Â Â Â Â Â B Î± I

2- The current-carrying conductor of the observation point is inversely proportional to the distance from the wire orÂ Â Â Â Â Â Â B Î± 1 / r

Combining these two rules – B Î± I / r

Hence magnetic field B = kI / r Newton / Ampere-meter

Where k is a directly proportional constant whose value is Î¼_{0}/ 2Ï€ = 2 Ã— 10-7 Newton/Ampere^{2}.

Î¼0 is called the permeability of a vacuum.

Hence B =Î¼_{0 }I / 2Ï€r = 2 Ã— 10-7 Ã— I / r Newton/Ampere^{2}.

### Magnetic Effect of Electric Current in a Straight Current-Carrying Wire

When an electric current flows in a straight current-carrying wire, the magnetic field is generated around it, it can be proved by the following experiment:

Spreading iron filings on flat cardboard makes a conductor wire vertical by making a hole in the middle, as per the circuit given in the following diagram, when the current flows through the conductor wire in the conductor, the iron filament slowly moves around the conductor wire. Takes the form of a circle. Which represents the direction of magnetic force lines.