Question:
In the figure shown, the magnetic field induction at the point O will be
In the figure shown, the magnetic field induction at the point O will be
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In the figure shown, the magnetic field induction at the point O will be \includegraphics[width=0.5\linewidth]1phy.png \labelfig:placeholder
Updated On: Apr 15, 2026
- $\frac{\mu_{0}i}{2\pi r}$
- $(\frac{\mu_{0}}{4\pi})(\frac{i}{r})(\pi+2)$
- $(\frac{\mu_{0}}{4\pi})(\frac{i}{r})(\pi+1)$
- $\frac{\mu_{0}}{4\pi}\frac{i}{r}(\pi-2)$
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The Correct Option is B
Solution and Explanation
Step 1: Concept
Field due to a straight wire of infinite length is $\frac{\mu_{0}i}{4\pi r}$ if the point is on a line perpendicular to its length while at the centre of a semicircular coil is $\frac{\mu_{0}\pi i}{4\pi r}$.
Step 2: Analysis
The total magnetic field at O is the vector sum of fields due to the two straight sections ($B_a$ and $B_c$) and the semicircular section ($B_b$).
Step 3: Calculation
$$B = B_{a} + B_{b} + B_{c}$$ $$B = \frac{\mu_{0}}{4\pi}\frac{i}{r} + \frac{\mu_{0}}{4\pi}\frac{\pi i}{r} + \frac{\mu_{0}}{4\pi}\frac{i}{r}$$ $$B = \frac{\mu_{0}}{4\pi}\frac{i}{r}(\pi+2)$$
Step 4: Conclusion
Hence, the induction is $(\frac{\mu_{0}}{4\pi})(\frac{i}{r})(\pi+2)$ out of the page.
Final Answer: (B)
Field due to a straight wire of infinite length is $\frac{\mu_{0}i}{4\pi r}$ if the point is on a line perpendicular to its length while at the centre of a semicircular coil is $\frac{\mu_{0}\pi i}{4\pi r}$.
Step 2: Analysis
The total magnetic field at O is the vector sum of fields due to the two straight sections ($B_a$ and $B_c$) and the semicircular section ($B_b$).
Step 3: Calculation
$$B = B_{a} + B_{b} + B_{c}$$ $$B = \frac{\mu_{0}}{4\pi}\frac{i}{r} + \frac{\mu_{0}}{4\pi}\frac{\pi i}{r} + \frac{\mu_{0}}{4\pi}\frac{i}{r}$$ $$B = \frac{\mu_{0}}{4\pi}\frac{i}{r}(\pi+2)$$
Step 4: Conclusion
Hence, the induction is $(\frac{\mu_{0}}{4\pi})(\frac{i}{r})(\pi+2)$ out of the page.
Final Answer: (B)
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