Find the Magnetic Field near a current-carrying straight wire

You must be familiar with the famous compass needle deflection experiment that forms the basics of magnetism. Whenever a compass is placed near a current-carrying conductor, the compass needle shows a deflection.

You will find various shapes of current-carrying conductors. The shapes and structures of these conductors are the deciding factors for the magnetic field.

In this article, you will get to know about the long straight wire magnetic field. In order to understand this topic in more detail, keep reading this article to get all your answers. 

What is a magnetic field?

The field generated by magnets is known as the magnetic field. Every magnet has its capacity for generating magnetic fields. The more the magnet’s magnetic field, the stronger the magnet is. There are usually various types of magnets, like horseshoe magnet, bar magnet and many more. The direction of the magnetic field of a bar magnet is like as follows,

• North to South direction outside
• South to North direction inside

Moving charges – magnetic fields

The magnetic field is produced by a charge which is moving. The current-carrying conductor has immense ability to produce magnetic fields around it. Whenever you need to find the direction of an electric field, then the right-hand thumbs rule is applied. This is a very useful way to find the direction of the magnetic field in current carrying loops. 

What is the Right-Hand thumb’s rule?

If you wish to locate the direction of a magnetic field of a straight current-carrying conductor, then follow these steps.

• Place your thumb in the direction of the flow of current.
• Now curl your fingers at your convenience.
• The direction of your fingers will determine the direction of the magnetic field. 

Biot-Savart Law

 A French scientist discovered this law in the late ’70s. One of the basic laws of magnetism. The main motto of this law is to create a relationship between the magnetic field and the electric field.

This law has influenced a lot of scientists to discover something new in the field of magnetism. This law states that whenever a current-carrying conductor is placed in a magnetic field, then the magnetic field is

• Directly proportional to the strength of the current
• Directly proportional to the length of the conductor
• Inversely proportional to the square of the distance between them
• Directly proportional to the angle between the direction of current and the line joining the element.

The formula for Biot Savart’s law is

B=04Idlsinr2

Where, 

I is the current of the conductor

dl is the small element of the long straight wire

r is the distance between the current element and the point

0 is a constant and permeability 

Mathematical Expression of Biot-Savart law

Consider a long straight wire carrying a current of magnitude I placed in a magnetic field. Let us consider a small section of that conductor and term it as dl. Consider a point r distance away from the conductor having dB as the magnetic field. 

The magnetic field due to this point will be, 

dB = 04Idlsinr2

What is Ampere’s Law?

This law is only applicable to closed conductors. This law states that the line integral of the magnetic field forming a closed loop around a current-carrying wire in the plane normal to the current, is equal to the μo times the net current passing through the closed loop. 

The formula of this law is given as.

B.dl=0I

Where,

I is the current through the conductor

B is the magnetic field of the closed loop

dl is the length of a small portion of the conductor

0 is a constant and permeability

What is the Amperian Loop?

Whenever you need to calculate the electric field around a closed current-carrying conductor, then Ampere’s law is applied to it. To apply Ampere’s law, you need to draw an Amperian loop around the closed conductor, which is an imaginary conductor. 

Explanation of how to find the magnetic field near a current-carrying straight wire

Let there be a current-carrying conductor having current I from point P and the distance between  them is ‘a’. An element dx is selected on the long straight wire. 

The magnetic field at the point P due to dx is,

dB=4Idxcosr2

Let, 

r = asecθ 

and x = a tanθ 

so that, dx = sec θ dθ

dB=I4asind

On integrating this from –/2 to /2

B=I2a

Conclusion

There are three steps in the learning process – learn, implement and write. Unless and until you perform all three steps effectively, you won’t be able to learn anything. With the help of this article, you will learn about Biot Savart law, ampere’s law, the Amperian loop along a magnetic field near a straight current-carrying conductor.