A Helmholtz coil is a device for producing a region of the nearly uniform magnetic field. It consists of two identical circular magnetic coils. Consider a circular current-carrying coil carrying current I.
From equation-(i) it is seen that the magnetic field varies with varying a distance from center to at any point along the axis. It is seen that from the above graph the magnetic field due to a single circular current-carrying coil cannot be uniform.
Helmholtz found that when two identical co-axial circular current-carrying coil carrying current in the same direction is placed at a distance that is equal to the radius of the coil, the magnetic field due to the coil is uniform. It is due to the magnetic field of one coil balanced by the magnetic field of another coil. i.e. if the magnetic field of one coil is decreased then the magnetic field of the other coil is increased and the net magnetic field remains constant.
The magnetic field due to circular current-carrying coil having n number of circular turns carrying current I at a distance x from the center of the coil is
The rate of increasing or decreasing of the magnetic field is given by differentiating b with respect to
x, we get
Since the magnetic field is uniform then dB/dx is constant.
The magnitude of the magnetic field is maximum in the midway of the space between two current-carrying coils,
We know that,