Question:
If the current 'i' is passing through the wire, it has a shape as shown in the figure. The radius of the curved part is R and the linear part is assumed to be very long. The magnetic induction of the field at the point O, is
(\(\mu _{0}=\)permeability of free space)
If the current 'i' is passing through the wire, it has a shape as shown in the figure. The radius of the curved part is R and the linear part is assumed to be very long. The magnetic induction of the field at the point O, is
(\(\mu _{0}=\)permeability of free space)
(\(\mu _{0}=\)permeability of free space)
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Add the field of the two semi-infinite straight parts and the semicircle. All three point the same way at O.
Updated On: Nov 12, 2026
- \(\frac{\mu _{0}i}{2\pi R}\left(2+\frac{\pi }{2}\right)\)
- \(\frac{\mu _{0}i}{4\pi R}(2+\pi )\)
- \(\frac{\mu _{0}i}{2\pi R}\left(1+\frac{3\pi }{2}\right)\)
- \(\frac{\mu _{0}i}{\pi R}\left(1+\frac{\pi }{2}\right)\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
The wire is a semicircle of radius R with two long straight parts leaving its ends. O lies on the perpendicular through the end of each straight part.
Step 2: Each part
Each semi-infinite straight wire gives \(\dfrac{\mu_{0}i}{4\pi R}\) at O.
The semicircle gives \(\dfrac{\mu_{0}i}{4R}\).
Step 3: Total
All three fields point the same way, so
\(B=2\cdot\dfrac{\mu_{0}i}{4\pi R}+\dfrac{\mu_{0}i}{4R}=\dfrac{\mu_{0}i}{4\pi R}(2+\pi)\)
Final Answer:
The magnetic induction at O is \(\frac{\mu_{0}i}{4\pi R}(2+\pi)\). \[ \boxed{\text{(B) }\dfrac{\mu_{0}i}{4\pi R}(2+\pi)} \]
The wire is a semicircle of radius R with two long straight parts leaving its ends. O lies on the perpendicular through the end of each straight part.
Step 2: Each part
Each semi-infinite straight wire gives \(\dfrac{\mu_{0}i}{4\pi R}\) at O.
The semicircle gives \(\dfrac{\mu_{0}i}{4R}\).
Step 3: Total
All three fields point the same way, so
\(B=2\cdot\dfrac{\mu_{0}i}{4\pi R}+\dfrac{\mu_{0}i}{4R}=\dfrac{\mu_{0}i}{4\pi R}(2+\pi)\)
Final Answer:
The magnetic induction at O is \(\frac{\mu_{0}i}{4\pi R}(2+\pi)\). \[ \boxed{\text{(B) }\dfrac{\mu_{0}i}{4\pi R}(2+\pi)} \]
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