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Question
Explain Ampere’s circuital law.
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Solution
Ampere’s law is the generalisation of Biot-Savart’s law and is used to determine magnetic field at any point due to a distribution of current. Consider a long straight current carrying conductor XY, placed in the vacuum. A steady current ‘I’ flows through it from the end Y to X as shown in the figure
Imagine a closed curve (amperian loop) around the conductor having radius 'r'. The loop is assumed to be made of a large number of small elements each of length `vec(dl)`. Its direction is along the direction of the traced loop.
Le `vecB`be the strength of magnetic field around the conductor. All the scalar products of ` vecB` and `vec(dl)` given the product of `mu_0` and I. It is given by `ointvecB.vec(dl) = ointBlcostheta` where, theta = angle between `vecB` and `vec(dl)`
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