Question

The magnetic field of given length of wire for single turn coil at its centre is $B$ then its value for two turns coil for the same wire is :-

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

Answer 1

Answer: (C)

The magnetic field at the center of the coil is given by $B =\frac{\mu I }{2 a }$
where $a$ and $n$ is radius and no. of turn respectively
Total lenght of a coil is $L$
in 1 turn the radius is $2 \pi a = L$
$\Rightarrow a =\frac{ L }{2 \pi}$
if no. of turn become twice than
$\Rightarrow 4 \pi r = L$
$\Rightarrow r =\frac{ L }{4 \pi}=\frac{ a }{2}$
$n =2$, radius become $\frac{ a }{2}$
$\Rightarrow B _{1}=\frac{ u 2 I }{\frac{ a }{2}}=\frac{4 \mu nI }{ a }=4 B$
hence the magnetic field become $4B$