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 $B=\frac{\mu I}{2a}$
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 $\frac{a}{2}$
$\Rightarrow B_1=\frac{u2I}{\frac{a}{2}}=\frac{4\mu nI}{a}=4B$
hence the magnetic field become $4B$