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Derive equation of missing term in Ampere circuital law. Write its definition and unit. |
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Answer» Solution :1. There is an alternative and appealing way in which the Biot-Savart.s law may be expressed. 2. As shown in figure, Ampere.s circuital law considers an OPEN surface with a boundary.  3. The surface has current passing through it. We consider the boundary to be made up of a number of small line elements. Consider ONE such element of length dl. 4. We take the value of the tangential component of the magnetic field `B_(T)` at this element and MULTIPLY it by the length of that element dl, `B_(T)dl=vecB*vec(dl)` = `B_(T)dlcos0^(@)` = `B_(T)dl` 5. The sum then tends to an integral. 6. Ampere.s circuital law : The line integral of magnetic induction over a closed loop in a magnetic field is equal to the product of algebric sum of electric currents enclosed by the loop and the magnetic permeability. `thereforeointvecB*vec(dl)=mu_(0)sumI` 7. Where `sumI` is the total current through the surface. 8. Let L be the length of the loop for which `vecB` is tangential and `I_(e)` be the current enclosed by the loop. `thereforeointvecB*vec(dl)=BLandsumI=I_(e)` `therefore` According to Ampere.s circuital law BL = `mu_(0)I_(e)` 9. The boundary of the loop chosen is a circle and magnetic field is tangential to the circumference of the circle, then Ampere.s law, `Bxx2pir=mu_(0)I` `thereforeB=(mu_(0)I)/(2pir)` 10. The Ampere.s law INVOLVES a sign-convention given by the right hand rule. 11. Let the fingers of the right hand be curled in the sense the boundary is traversed in the loop integral `ointvecB*dvecl`. 12. Then the direction of the thumb gives the sense in which the current I is regarded as positive. |
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