Question

Write about the Magnetic field at the centre of a circular current carrying loop.. Please try to write the explanation with formula..​

Answer 1

Consider a circle of radius R and current I

db= μo/4π {I(dl×r)/r^3}

Consider a element of angle dθ and of length dl=Rdθ

db=μo/4π {I(Rdθ)Rsin90}/R ^3

for total field

B=∫db limit from 0 to θ

B =(μoI/4πR)θ

∴ for full circle θ=2π

B=μοI/2R

So basically,

Electric current in a circular loop creates a magnetic field which is more concentrated in the center of the loop than outside the loop. Stacking multiple loops concentrates the field even more into what is called a solenoid.

Hope this helps you...

Answer 2

Magnetic Field at the centre of a circular current carrying Loop :

Consider a current carrying circular loop in which the magnetic field is at the centre.

Let ,

Radius of the loop = r

Current in the loop = I

B, Magnetic field, at perpendicular in the centre.

By the Biot Savart's Law , we got the magnitude of B (attachment).

After integration we get the exact value of magnetic field (attachment).

Here , if the coil loop has N number of turns than the value of b will get Multiplied to N.

The Magnetic Field B is perpendicular to the loop , thus directed upward (right hand palm rule ) ...

As the direction of current changes ,the direction of magnetic field will also changes.

Here if the Direction of current is reversed , then the direction of magnetic field will be downward.