Magnetic field at a point on the axis of a circular coil carrying current
In this topic we will discuss about Magnetic field at a point on the axis of a circular coil carrying current , and using its derivation we can find the magnetic field and we will also discuss about magnetic moment due current carrying coil.
Magnetic field at a point on the axis of a circular coil carrying current –
Suppose a circular coil of radius ‘a’ with center ‘O’ . Let current I is flowing through the coil we have to find the magnetic field at point ‘P’ , which is x distance away from the center .
Suppose two small element ‘dl’ of the coil C and D which is diametrically opposite points as shown in figure.
Here PC =PD = √(a2+x2), and we consider <COP = ɸ = <DPO .
As shown in figure dBcosɸ is cancelled by each other , then the net magnetic field dB sinɸ will be in the same side .
Here magnetic field due to small current carrying element dB = (µ0/4Π) I dl sinθ/r2 ; here r=√(a2+x2),
So we can write , dB=(µ0/4Π) Idl sinθ/(a2+x2) ,
So magnetic field at point p due to the circular loop
Special case 1- when point P lies at the center of the circular coil then , x = 0
Then B= (µ0/4Π) 2∏nI/a = µ0nI/2a ,
Case 2 – When point P is far away from the center then a2+x2=x2
Then B= (µ0/4Π) 2nIA/x3 [ since ∏a2 = A (area)]
Here nIA= M (magnetic moment)
So we can write , B= (µ0/4Π) 2M/x3
So we can define the magnetic moment due to current carrying coil is given as the product of ampere turns and area of current loop . SI unit of magnetic moment is A-m2 .
To watch the video related to this topic, Magnetic field at a point on the axis of a circular coil carrying current ( By Nayan jha sir) go to the link given below-
The polarity of magnetic dipole due to the current loop is decided as , if the current from one side is clock wise direction it gives south pole and on another face direction of current is anti-clock wise it gives north pole , as shown in figure-
Case 3- The variation of magnetic field induction with distance of a point on the axis of coil carrying current is given as –
class 12th physics syllabus removed . How it is beneficial for the students , see the video given below-