A wire of length \( L \) carrying current \( I \) is bent into a circular loop. The magnetic field at the center of the loop is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \displaystyle\frac{\mu_{0}I\pi}{L} \)
The field at the centre of a circular loop of radius r is \( B = \mu_0I/2r \). Bending the wire into a loop makes its whole length the circumference.
\( L = 2\pi r \Rightarrow r = L/(2\pi) \)
\( \displaystyle B = \frac{\mu_0I}{2r} = \frac{\mu_0I}{2}\times\frac{2\pi}{L} = \frac{\mu_0I\pi}{L} \)