State and explain Biot-Savart’s law
In this topic we will discuss about Biot-savart’s law and magnetic field at a point due to finite current carrying wire or conductor.
Biot- Savart law – Biot-Savart’s law explain the magnetic field due to small current carrying element
As we know , whenever the current passes through a conductor magnetic field setup around it . To find the magnetic field at any point first given by Jean Biot and Felix savart . according to Biot- Savart , magnetic field intensity at any point due to small current carrying element is given as dB=µ0idl sinθ/r2 .
EXPLANATION- Let us consider a small element of length ‘dl’ carrying a current I through it . If dB is the magnetic field at a point r distance away from the element , then according to this law
- dB α I …………………….1
- dB α dl …………………2
- dB α sin θ …………….3
- dB α 1/r2 ………………4
after combining these equations ,we get
dB α I dl sinθ/r2
so , dB= k I dl sinθ/r2
(Where K= µ0/4Π = 10-7 Wb/ (A m ))
Magnetic field due to straight current carrying wire of finite length –****( derivation is not in syllabus for 12th board examination, but we must know the result )
Suppose current ‘I’ is flowing through a wire XY , and we have to find the magnetic field at point ‘P’.as shown in figure .
B = (µ0I/4Πa)(sinɸ1 + sinɸ2) ,
Special cases – Case-(1) — When the wire is of infinite length and point P is near the wire in that case ɸ1=900 , ɸ2=900 ;
So magnetic field at that point P , B = (µ0I/4Πa)(sin90 + sin90) = µ0I/2Πa
Case-(2)– When the wire is of infinite length and point P is near the one end of the wire in that case ɸ1=900 , ɸ2=00 ;
So magnetic field at the point P , B = (µ0I/4Πa)(sin90 + sin0) = µ0I/2Πa ;
Case-(3)—If length of the conductor is finite (L) and point P lies on right bisector of conductor , then ɸ1=ɸ2= ɸ ; and sinɸ=L/( 4a2+L2)1/2 .
Then magnetic field B= (µ0I/4Πa)(sinɸ + sinɸ)= (µ0I/4Πa)2sinɸ=(µ0I/4Πa)[ L/( 4a2+L2)1/2];
Direction of magnetic field – The direction of magnetic field through a current carrying wire can be found using right hand thumb rule .
Right hand thumb rule – According to this rule we held the current carrying straight wire in our hand grip of our right hand so that thumbs directed towards the direction of flow of current then the curled finger gives the direction of magnetic field around the conducting wire . As shown in figure.
to see the video on Biot-Savart’s law click on the link given below-