Magnetic Field of Current Loop

Examining the direction of the magnetic field produced by a current-carrying segment of wire shows that all parts of the loop contribute magnetic field in the same direction inside the loop.

Electric current in a circular loop creates a magnetic field which is more concentrated in the center of the loop than outside the loop. Stacking multiple loops concentrates the field even more into what is called a solenoid.

Field at center

Field on axis

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Magnetic field concepts

Currents as magnetic sources

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Field at Center of Current Loop

The form of the magnetic field from a current element in the Biot-Savart law becomes

which in this case simplifies greatly because the angle =90 ° for all points along the path and the distance to the field point is constant. The integral becomes

The current used in the calculation above is the total current, so for a coil of N turns, the current used is Ni where i is the current supplied to the coil.

The Earth's magnetic field at the surface is about 0.5 Gauss.

Discussion of current loop

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Magnetic field concepts

Currents as magnetic sources

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Field on Axis of Current Loop

Show geometric details

The application of the Biot-Savart law on the centerline of a current loop involves integrating the z-component.

The symmetry is such that all the terms in this element are constant except the distance element dL , which when integrated just gives the circumference of the circle. The magnetic field is then

Calculation

Discussion of current loop

Index

Magnetic field concepts

Currents as magnetic sources

HyperPhysics***** Electricity and Magnetism

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Geometry: Field on Axis of Current Loop

Discussion of current loop

Index

Magnetic field concepts

Currents as magnetic sources

HyperPhysics***** Electricity and Magnetism

R Nave

Go Back