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CBSE Class 12-science Answered

ampere law
Asked by shantanumail24 | 09 Mar, 2022, 07:04: PM
answered-by-expert Expert Answer
It is known that there is magnetic field around a current carrying conductor.
Magnitude and direction of magnetic field induction at a given point are determined from Biot-Savort's law.

Ampere's Circuital law states that in any closed loop which encloses a long current carrying conductor ,
if the closed loop is considered to be made up of small segments each of length ds , then sum of product of ds and
component of magnetic field induction parallel to  segment ds equals the product of magnetic permeability and the
magnitude of current passing through long conductor.
 
Statement of Ampere's law expressed mathematically as
 
begin mathsize 14px style sum for blank of B subscript vertical line vertical line end subscript space d s space equals space mu space I end style
If the segment length ds is infinitesimally small , then above expression can be written as
 
begin mathsize 14px style contour integral space B times d s space equals space mu space I end style
This statement of Ampere's law is shown in fig(a)
 
If the closed loop encloses many number of current carrying conductors , then Ampere's law is given as
 
begin mathsize 14px style contour integral space B times d s space equals space mu sum for blank of space I end style
 
-----------------------------------------
 
Let us take a specific case as shown in fig. (b) .
 
A closed loop of radius R is considered around a long current carrying conductor so that
the coductor is passing through centre of closed loop and is perpendicular to the plane of closed loop .
 
Then by Ampere's law .
 
begin mathsize 14px style contour integral space B times d s space equals space B space cross times left parenthesis space 2 pi space R space right parenthesis space equals space mu space I end style  ............................(1)
where B is magnetic field induction at radial distance R .
Direction of this magenetic field is along the tangent of closed loop.
 
Above expression is used to get magnetic field induction  near a long current carrying conductor.
 
Magnetic field induction B at a distance d from long current carrying conductor is given as
 
begin mathsize 14px style B space equals space fraction numerator mu space I over denominator 2 pi space d end fraction end style
( distance d is substituted to R  in eqn.(1) )
Answered by Thiyagarajan K | 09 Mar, 2022, 10:05: PM

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