Question

fin the expression of magnetic field produced at the center of current carrying circular coil.

Answer 1

At the center of a current carrying coil, the magnetic field intensity is directly proportional to the current and inversely proportional to the radius of the coil.

So, if the current is doubled and radius is halved, then the value of B increases by 4 times the initial value.

Answer 2

Hi,
Here's your Answer,

Magnetic field at the center

The distance between current element on the circular coil and the center is ‘r’ and the angle between current element and ‘r’ is 90o.

Circular Coil

By applying Biot Savart’s Law –


dB = μ04/π . idlsinθ/r^2

Here,

θ = 90o

∴ dB = μ0/4π . idlsin90/r^2

∴ dB = μ0/4π . idl/r^2

The complete circular coil is a combination of multiple current elements. So to find the resultant magnetic field due to all the current elements at the center we need to integrate dB.

∫ dB = ∮ μ0/4π . idl/r^2

B = μ0/4π . i/r^2 . 2πr

B = μ0i/2r

Direction of magnetic field at the centre is outwards.


Hope It Helped You !!!!!