Consider a circular coil of radius a carrying a steady current I. Let it be placed with its center at origin and plane perpendicular to the X axis.
Now imagine a small element AB of length dl. The magnetic field at a point P on the X axis at a distance x from the origin is given by
where r is the distance between the element and the point P.
If vector r makes an angle alpha with the X axis, then dB will be inclined to the +Y axis. Hence dB can be resolved into X and Y components given by
Now if we consider an identical element CD diametrically opposite to AB, the magnetic field due to CD will be in a direction inclined to the Y axis.
The above expressions makes it clear that the Y component of magnetic field due to diametrically opposite identical elements cancels each other. Hence the net magnetic field at P is simply the vector sum of x components of all the elements of the ring.
Thus the magnetic field due to a coil at a point on the x axis depends on the current I, the radius of the coil and the distance of the point from the center.
If the point P selected at the center of the coil then x=0
The direction of magnetic field due to a circular coil is obtained by the right hand thumb rule which is stated as follows:
Curl the palm of right hand around the circular coil with the fingers pointing in the direction of current. Then the extended thumb gives the direction of magnetic field.
Thus an anti-clock wise current gives a magnetic field out of the coil and a clock wise current gives a magnetic field into the coil.
Now imagine a small element AB of length dl. The magnetic field at a point P on the X axis at a distance x from the origin is given by
where r is the distance between the element and the point P.
If vector r makes an angle alpha with the X axis, then dB will be inclined to the +Y axis. Hence dB can be resolved into X and Y components given by
Now if we consider an identical element CD diametrically opposite to AB, the magnetic field due to CD will be in a direction inclined to the Y axis.
The above expressions makes it clear that the Y component of magnetic field due to diametrically opposite identical elements cancels each other. Hence the net magnetic field at P is simply the vector sum of x components of all the elements of the ring.
Thus the magnetic field due to a coil at a point on the x axis depends on the current I, the radius of the coil and the distance of the point from the center.
If the point P selected at the center of the coil then x=0
The direction of magnetic field due to a circular coil is obtained by the right hand thumb rule which is stated as follows:
Curl the palm of right hand around the circular coil with the fingers pointing in the direction of current. Then the extended thumb gives the direction of magnetic field.
Thus an anti-clock wise current gives a magnetic field out of the coil and a clock wise current gives a magnetic field into the coil.
Current loop as a magnetic dipole
In the preceeding section we have seen that anti clock wise current gives outgoing flux, indicating south polarity. In short a current loop gives north polarity on one side and south polarity on the other side resulting in a magnetic dipole.
The magnetic dipole moment of a current loop is defined as the product of electric current and area.Its SI unit is Am2.
Now magnetic field at a point on the axis of a circular coil given by the equation 10 can be rewritten as
The above equation is similar to that of the electric field on the axial line of an electric dipole. This we can conclude that a current loop is equivalent to a magnetic dipole of moment equal to m=IA. This can be generalized to any geometric shape of the current loop.
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| Magnetic Field due to a long straight current carrying conductor |
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| Ampere's Circuital Law |
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