Question

A current-carrying circular coil is bent so as to convert it into a double loop. Both the loops are concentric and are carrying current in the same direction. If initially, $B$ is the magnetic field at the centre of the coil, then finally magnetic field at the centre will be

• A. zero
• B. $B$
• C. $2B$
• D. $4B$

Answer 1

Answer: (D)

Let's assume that the current in the coil is Initially the field at the centre is $i$ and the radius of the coil is $r$ , then the initial magnetic field at the centre is
$B_{initial}=\frac{\mu _{0} i}{2 r}$
When we make two loops out of one, we are basically making a coil of half the radius and double the number of turns, so
$B_{final}=2\frac{\left(\mu \right)_{0} i}{2 \left(r/2\right)}=\frac{2 \left(\mu \right)_{0} i}{r}\Rightarrow B_{final}=4B_{initial}=4B$