Magnetic field at a point on the axis of a circular coil carrying current

Magnetic field at a point on the axis of a circular coil carrying current

Before to learn about this topic students must know about Biot-Savart law. To learn about this topic click here-

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.

To get the notes on magnetic field at the center of a circular current carrying coil, click here-

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-

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