Question

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

(1) \(\frac{\mu_0i}{4R}\) pointed away from the page

(2) \(\frac{\mu_0i}{4R} \left[1 - \frac 2 \pi \right]\) pointed away from page

(3) \(\frac{\mu_0i}{4R} \left[1 - \frac 2 \pi \right]\) pointed into the page

 (4) \(\frac{\mu_0i}{4R}\) pointed into the page

Answer 1

Correct option is (2) \(\frac{\mu_0i}{4R} \left[1 - \frac 2 \pi \right]\) pointed away from page

\(B = \frac{\mu_0}{4\pi} \frac IR (\pi) - \frac{\mu_0}{4\pi} \frac {2I}R \)

\(=\frac{\mu_0i}{4R} \left[1 - \frac 2 \pi \right]\) outward i.e. away from page.