Question

A wire carrying current I has the shape as shown in the adjoining figure. Linear parts of the wire are very long and parallel to X–axis while the semicircular portion of radius R lies in the Y-Z plane. Magnetic field at point O is: 

• A. \(\vec{B}=\dfrac{\mu_0 I}{4\pi R}(\pi \hat{i}\times 2\hat{k})\)
• B. \(\vec{B}=\dfrac{\mu_0 I}{4\pi R}(\pi \hat{i}+2\hat{k})\)
• C. \(\vec{B}=\dfrac{\mu_0 I}{4\pi R}(\pi \hat{i}-2\hat{k})\)
• D. vecB=(mu₀ I)/(4π R)(hati+2hatk)

Hint:

Use right–hand thumb rule separately for curved and straight current elements.

Answer 1

The Correct Option is B

Step 1: Magnetic field due to semicircular arc: Bₐrc=(mu₀ I)/(4R) Direction is along +hati.
Step 2: Magnetic field due to two long straight wires: Bₛtᵣₐᵢght=2((mu₀ I)/(4π R)) Direction is along +hatk.
Step 3: Net magnetic field: vecB=(mu₀ I)/(4π R)(π hati+2hatk)