2023 Moving Charges and MagnetismBiot-Savart Law – Field due to Straight Wires and Arc Hard Question 1 of 5 in Biot-Savart Law – Field due to Straight Wires and Arc

A very long conducting wire is bent in a semi-circular shape from A to B as shown in figure. The…

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:

A $\frac{\mu_0 i}{4R}\left[1-\frac{2}{\pi}\right]$ pointed into the page
B $\frac{\mu_0 i}{4R}$ pointed into the page
C $\frac{\mu_0 i}{4R}$ pointed away from the page
D $\frac{\mu_0 i}{4R}\left[1-\frac{2}{\pi}\right]$ pointed away from page

The answer is D.

Solution

Semicircle gives $\frac{\mu_0 i}{4R}$ and the two straight wires each give $\frac{\mu_0 i}{4\pi R}$ in the opposite sense.

$\vec{B}_P=\vec{B}_{upper\ wire}\otimes+\vec{B}_{semi-circle}\odot+\vec{B}_{lower\ wire}\otimes$ $B_P=-\frac{\mu_0 i}{4\pi R}+\frac{\mu_0 i}{4R}-\frac{\mu_0 i}{4\pi R}$ $=\frac{\mu_0 i}{4R}\left(1-\frac{2}{\pi}\right)$ pointing away from the page

Concept field at centre of semicircular bend

Biot-Savart Law – Field due to Straight Wires and Arc in past papers

5 questions from this chapter have appeared across 5 exam years.