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प्रश्न
Explain Ampere’s circuital law.
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उत्तर
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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संबंधित प्रश्न
Write Maxwell's generalization of Ampere's circuital law. Show that in the process of charging a capacitor, the current produced within the plates of the capacitor is `I=varepsilon_0 (dphi_E)/dt,`where ΦE is the electric flux produced during charging of the capacitor plates.
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(Statement of the law is not required).
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Read the following paragraph and answer the questions.
|
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Magnetic fields are produced by:
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According to Ampere's Circuital Law, the line integral \[\oint\vec{B}\cdot d\vec{l}\] taken around any closed loop equals:
Substituting \[B=\frac{\mu_0 I}{2\pi r}\] into \[\oint\vec{B}\cdot d\vec{l}=B(2\pi r)\] for a straight wire yields:
In the sign convention for Ampere's law, if the fingers of the right hand curl along the direction of integration (\[d\vec{l}\]), the thumb points:
