Question:
A current \(i\) is flowing in a straight conductor of length \(L\). The magnetic induction at a point on its axis at a distance \(\frac{L}{4}\) from its centre will be :
A current \(i\) is flowing in a straight conductor of length \(L\). The magnetic induction at a point on its axis at a distance \(\frac{L}{4}\) from its centre will be :
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Use the Biot-Savart law: the field of a current element depends on \(\sin\theta\), the angle between \(d\vec{l}\) and the line joining the element to the point.
Updated On: Oct 31, 2026
- Zero
- \(\frac{\mu_0 i}{2\pi L}\)
- \(\frac{\mu_0 i}{\sqrt{2}L}\)
- \(\frac{4\mu_0 i}{\sqrt{5}\pi L}\)
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The Correct Option is A
Solution and Explanation
Biot-Savart law: \(dB = \frac{\mu_0}{4\pi}\frac{i\,dl\,\sin\theta}{r^2}\).
A point on the axis of the straight conductor lies along the line of the current, so for every element \(d\vec{l}\) the position vector \(\vec{r}\) is parallel (or antiparallel) to \(d\vec{l}\).
Hence \(\theta = 0^\circ\) or \(180^\circ\) and \(\sin\theta = 0\) for every element.
So \(d\vec{B} = 0\) for each element and the total field is zero.
Answer: (1) Zero
A point on the axis of the straight conductor lies along the line of the current, so for every element \(d\vec{l}\) the position vector \(\vec{r}\) is parallel (or antiparallel) to \(d\vec{l}\).
Hence \(\theta = 0^\circ\) or \(180^\circ\) and \(\sin\theta = 0\) for every element.
So \(d\vec{B} = 0\) for each element and the total field is zero.
Answer: (1) Zero
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