Question

A circular loop is given in figure with current I and having radius R. Find the
value of magnetic induction at its centre.​

Answer 1

Answer:

We have a ring of radius R carrying current I as shown in the following figure.

We will take an element on ring of length dl, r is the position vector of point P from the element dl. In the front view, we can see that horizontal component will cancel each other. Only vertical will add up and will give net magnetic field.

Using Biot-savart law:-

Magnetic field at point P due to element dl=dB=(4πμ0I)r2dl

Vertical component =(dB)sinα

Net magnetic field =BNet=∫(dB)sinα

⇒BNet=∫(4πμ0I)r2dlsinα=4πμ0I∫rR×r21dl 

⇒BNet=4πr3μ0IR∫dl;  

since ∫dl=2πR

⇒B