KEAM 2019 Physics and Chemistry Paper

A circular loop of radius R and current I is shown in the figure below From Biot-savart law, the magnetic field at some point in space at distance R is given as,
dB=‌

µ0

4π

i‌

dl×P

R3

Since, the loop is circular in shape so,
=2πR
Now integrating the field in whole length of wire loop
⇒‌‌

B

∫

0

dB=‌

µ0

4π

‌

iR

R3

‌

2πR

∫

0

dl
⇒‌‌B=‌

µ0

4π

‌

i

R2

2πR=‌

µ0i

2R

Also, with help of right hand thumb rule, we can conclude, that the magnetic field is in +z direction.
⇒‌‌B=‌

µ0i

2R

⋀

z