

BIOT
SAVART LAW


Consider a long straight conductor carrying current I. Then magnetic field is in the form of circle. BIOT SAVART found that the magnitude of field B is directly proportional to twice of current I and inversely proportional to the distance r. 

B a 2I And B a 2I/r B = m_{o}/4p.2I/r 

m_{o}
is called permeability of free space. m_{o}/4p is proportionality constant. Its value is 10^{7}. 

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AMPERE’S
LAW


STATEMENT: This law states: "The sum of products of tangential component of B and length element Dl of a closed curve is m_{o} times the current enclosed." m_{o} = permeability of free space. Its value is 4p*10^{7}. Its unit is Henry/m^{2}. Mathematically. 

S(B.Dl)
= m_{o}I


PROOF
OF AMPERE’S LAW


Let the circular field B be divided in to small elements Dl. Now tangential component of B 

Bx = BCosq


Multiplying length element Dl with tangential component of B, we have,  
B. Dl = BCosq. Dl But, q is negligible i.e. q = 0 B. Dl = BCos(0^{o}). Dl B. Dl = B (1) . Dl B. Dl = B. Dl 

For the complete curve, the sum of their products will be,  
SB. Dl = SB. Dl = BS. Dl but, B = m_{o}/4p.2I/r and SDl = 2pr SB.Dl = m_{o}/4p.2I/r x 2pr SB.Dl = m_{o} x I 

This is mathematical form of Ampere’s law.  
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