A circular loop of 20 turns carries a current of 5.0 A. If the magnetic field at the centre of the loop is 1.57 mT, the radius of the loop would be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4 cm
The magnetic field (B) at the center of a circular loop of radius (r), carrying a current (I) and having N turns is -
$B=\frac{μ_0NI}{2r}$
Now,
$B=1.57×10^{-3}T$ [given]
$N=20$
$I=5.0A$
$r=\frac{μ_0NI}{2B}=\frac{4\pi×10^{-7}×20×5}{2×1.57×10^{-3}}$
$=4×10^{-2}=4cm$