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

• A

  $\frac{B}{4}$
• B

  $\frac{B}{2}$
• Correct answer
  C

  $4 B$
• D

  $2 B$

Solution

Here $B_1=B=\frac{\mu_0 I}{2 R}$ $\begin{aligned} & B_2=\frac{\mu_0(2 \mathrm{I})}{2 r} \\ & \therefore 2 \times 2 \pi r=2 \pi R \Rightarrow r=R / 2 \end{aligned}$ So, $B_2 = 4 B$

Hence, the correct answer is option: 'C'.