Question

State priot savarts law and use it to find magnetic field at the centre of a circular loop haring N turns of radius R each and carrying current I

Answer 1

Explanation ⇒  ''According to the Biot Savart law, the Magnetic field produced due to the small segment 'dl' carring current I at an distance of R, making angle θ is given as,''

             dB = μ₀/4π × idlSinθ/r²

DERIVATION

Now, Let us take an circular loop of Radius a. Carring current i, in clockwise direction.

Then Magnetic field at the centre of the circular loop is CROSS MAGNETIC FIELD. [By Right hand Palm Rule.]

Let us cut an small segment dl at the circular loop, which produces an magnetic field dB at the centre.

Then Applying Biot-Savart Law,

 dB =  μ₀/4π × idlSinθ/R²

dB = μ₀/4π × idl/R²    [Since, θ = 90°]

Integrating both sides,

∴ B = μ₀/4π × i/R² × 2πR

∴ B = μ₀/2 × i/R

For N no. of turns,

B = μ₀/2 × Ni/R

Hope it helps.

Answer 2

Answer:

According to the Biot Savart law, the Magnetic field produced due to the small segment 'dl' carring current I at an distance of R, making angle θ is given as,''

             dB = μ₀/4π × idlSinθ/r²

Explanation: