A straight conductor of length $32 \mathrm{~cm}$ carries a current of $30 \mathrm{~A}$. Magnetic induction at a point in air at a perpendicular distance of $12 \mathrm{~cm}$ from the mid-point of the conductor is

• A

  0.2 G
• B

  0.3 G
• Correct answer
  C

  0.4 G
• D

  0.5 G

Solution

$\beta=\frac{\mu_0 I}{4 \pi r}\left(\sin \theta_1+\sin \theta_2\right)$ $\begin{aligned} & =\frac{10^{-7} \times 30}{12 \times 10^{-2}}\left(2 \times \frac{16}{20}\right) \\ & =4 \times 10^{-5} \mathrm{~T} \\ & =0.4 \times 10^{-4} \mathrm{~T} \\ & =0.4 \mathrm{G}\end{aligned}$

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