 # Ampere's Law

In electromagnetism, Ampère’s circuital law relates the integrated magnetic field around a closed loop to the electric current passing through the loop. Ampere’s Law can be stated as:

“The magnetic field created by an electric current is proportional to the size of that electric current with a constant of proportionality equal to the permeability of free space.”

The equation explaining Ampere’s law which is the final Maxwell’s equation  is given below: Maxwell’s Equation

## Who was André-Marie Ampère?

André-Marie Ampère was a scientist who performed experiments with forces that act on current-carrying wires. The experiment was done in the late 1820s around the same time when Faraday was working on his Faraday’s Law. Faraday and Ampere had no idea that their work would be combined by Maxwell Himself four years later.

## What is Ampere’s Law?

According to Ampere’s law, magnetic fields are related to the electric current produced in them. The law specifies the magnetic field that is associated with a given current or vice-versa, provided that the electric field doesn’t change with time.

### What is Ampere’s Circuital Law?

Ampere’s circuital law can be written as the line integral of the magnetic field surrounding closed-loop equals to the number of times the algebraic sum of currents passing through the loop. Suppose a conductor carries a current I, then this current flow generates a magnetic field that surrounds the wire.

The equation’s left side describes that if an imaginary path encircles the wire and the magnetic field are added at every point, then it numerically equals to the current encircled by this route, indicated by Ienc.

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### Determining Magnetic Field by Ampere’s Law (Example)

Suppose you have a long enough wire that carries a constant current I in amps. How would you determine the magnetic field wrapping the wire at any distance r from the wire?

In the figure below ( Figure 1), a long wire exists that carries current in Amps. We need to find out how much is the magnetic field at a distance r. Therefore, we sketch an imaginary route around the wire indicated by dotted blue toward the right in the figure. Figure 1

According to the second equation, if the magnetic field is integrated along the blue path, then it has to be equal to the current enclosed, I.

The magnetic field doesn’t vary at a distance r due to symmetry. The path length (in blue) in figure 1 equals to the circumference of a circle, 2πr.

When a constant value H is added to the magnetic field, the equation’s left side looks like this: We have figured the magnitude of the field H. Since r is arbitrary, the value of the field H is known.

According to the equation, the magnetic field lowers in magnitude as we move wider. Hence, Ampere’s law can be applied to calculate the extent of the magnetic field surrounding the wire. The field H is a Vector field which reveals that each region has both a direction and a magnitude. The field’s direction is tangential at every point to the imaginary loops as shown in figure 2 and the right-hand rule finds the direction of the magnetic field. Figure 2

To know more about real-time applications of Ampere’s law along with Gauss law and magnetic field due to Solenoid, visit BYJU’S – The learning app.