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A helmholtz coil is a device for producing a region of nearly uniform magnetic field. Besides creating magnetic fields, helmholtz coils are used in scientific apparatus to cancel external magnetic fields, such as earth’s magnetic field. A helmholtz pair consists of two identical circular magnetic coils that are placed symmetrically along a common axis, one on each side of experimental area and separated by a distance equal to radius R of the coil. Each coil carries equal current in the same direction. Setting the distance between the coils h=R, is what defines a Helmholtz pair, it minimizes the non-uniformity of the field at the centre of the coils such that the first non-zero derivative is .

The calculation of exact magnetic field at any point in space is very complex. But field at any point on the axis can be calculated easily.

If number of turn in each coil is n and current is I then magnetic field at the midpoint between the coils is :

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ParagraphA helmholtz coil is a device for producing a region of nearly uniform magnetic field. Besides creating magnetic fields, helmholtz coils are used in scientific apparatus to cancel external magnetic fields, such as earth’s magnetic field. A helmholtz pair consists of two identical circular magnetic coils that are placed symmetrically along a common axis, one on each side of experimental area and separated by a distance equal to radius R of the coil. Each coil carries equal current in the same direction. Setting the distance between the coils h=R, is what defines a Helmholtz pair, it minimizes the non-uniformity of the field at the centre of the coils such that the first non-zero derivative is .

The calculation of exact magnetic field at any point in space is very complex. But field at any point on the axis can be calculated easily.

If number of turn in each coil is n and current is I then magnetic field at the midpoint between the coils is :

zandrare vertical and radial position coordinates respectively. Initially ring has no current flowing in it. When released it starts to move downwards with its axis still vertical and it performs harmonic oscillations for small displacement. Initiallyz= 0 for ring. Mass of the ring ism, radius isrand its inductance isL.Ring makes harmonic oscillations with amplitude: