Consider a long conductor carrying a steady current I. Let us now find the magnetic field on a point P at a distance 'a' away from the conductor. The long conductor can be imagined to be composed of very large number of small current elements. Now the magnetic field at the point is the vector sum of magnetic field due to all such current elements.
Let the perpendicular from P meet the conductor at O. Consider a small current element of length dl at a distance l below O. Let the current element make at an angle theta with the vector connecting dl and P.
Now the magnetic field at P due to the element is given by Biot-Savart law as
dB = (muzeroxIdl sin theta)/4xpiexrxr into the plane of the paper.
Now from the diagram we get
theta equal to 90-theta.
l equal to a tan theta
cos phi equal to a/r
using the above equations the variables in the Biot-Savarts law can be rewritten as
sin theta equal to sin(90- phi)=cos phi
The net magnetic field at P can be now obtained by integrating (4) between proper limits. The expression reveals that magnetic field due to a long straight conductor depends on current and the distance of the point from the conductor.
Now the direction of magnetic field can be obtained by a simple law known as right hand grip rule which is stated as follows:
Grasp the conductor in right hand with the extended thumb pointing in the direction of the current.Then the palm fingures around in the direction of the magnetic field.
Let the perpendicular from P meet the conductor at O. Consider a small current element of length dl at a distance l below O. Let the current element make at an angle theta with the vector connecting dl and P.
Now the magnetic field at P due to the element is given by Biot-Savart law as
dB = (muzeroxIdl sin theta)/4xpiexrxr into the plane of the paper.
Now from the diagram we get
theta equal to 90-theta.
l equal to a tan theta
cos phi equal to a/r
using the above equations the variables in the Biot-Savarts law can be rewritten as
sin theta equal to sin(90- phi)=cos phi
The net magnetic field at P can be now obtained by integrating (4) between proper limits. The expression reveals that magnetic field due to a long straight conductor depends on current and the distance of the point from the conductor.
Now the direction of magnetic field can be obtained by a simple law known as right hand grip rule which is stated as follows:
Grasp the conductor in right hand with the extended thumb pointing in the direction of the current.Then the palm fingures around in the direction of the magnetic field.
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| Biot-Savart's Law |
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| Magnetic Field due to a circular coil |
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