Question

As shown in the figure, a very long conducting wire is bent in a semi-circular shape from A to B. The magnetic field at point P for steady current configuration is given by:

• A. $\frac{\mu_0i}{4R}$ pointed away from the page
• B. $\frac{\mu_0i}{4R}[1-\frac{2}{\pi}]$ pointed away from the page
• C. $\frac{\mu_0i}{4R}[1-\frac{2}{\pi}]$ pointed into the page
• D. $\frac{\mu_0i}{4R}$ pointed into the page

Answer 1

Answer: (B)

$\frac{\mu_0i}{4R}[1-\frac{2}{\pi}]$ pointed away from the page

Answer 2

We know that,
$B=\frac{\mu_0}{4\pi}\frac{i}{R}(\pi)-\frac{\mu_0}{4\pi}\frac{2i}{R}$

$B=\frac{\mu_0i}{4R}[1-\frac{2}{\pi}]$ outdraw i.e away from the page

So, the correct option is (B): $\frac{\mu_0i}{4R}[1-\frac{2}{\pi}]$ pointed away from the page.