KEAM 2021 Physics and Chemistry Solved Paper

At a point situated at a distance r from the centre of a current carrying circular coil along the axial line, the magnetic field is given as
B=‌

µ0iR2

2(R2+r2)3∕2

where, i is the current in the coil and R is the radius of the coil.
Given, r=R
⇒‌‌B=‌

µ0iR2

2(R2+R2)3∕2

=‌

µ0i

2⋅23∕2R

....(i)
Since, magnetic field due to a current carrying circular coil at centre is given as
B=‌

µ0i

2R

=Bc (given) ...(ii)
From Eqs. (i) and (ii), we get
B=‌

Bc

2√2