Question:
Consider a circular loop (radius \(R\)) carrying current \(I\), the magnetic field produced by it at a point on the axis at a distance \(z\) from the centre of the loop is \(\frac{xR^{2}}{(z^{2}+R^{2})^{3/2}}\). The value of \(x\) is
Consider a circular loop (radius \(R\)) carrying current \(I\), the magnetic field produced by it at a point on the axis at a distance \(z\) from the centre of the loop is \(\frac{xR^{2}}{(z^{2}+R^{2})^{3/2}}\). The value of \(x\) is
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Recall the standard result for the on-axis field of a loop and compare the coefficient.
Updated On: Nov 12, 2026
- \(\mu _{0}I\)
- \(\frac{\mu _{0}I}{4}\)
- \(\frac{\mu _{0}I}{2}\)
- \(\frac{\mu _{0}I}{6}\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
The magnetic field on the axis of a circular loop of radius \(R\) carrying current \(I\) at distance \(z\) from its centre is \(B=\frac{\mu_{0}IR^{2}}{2(z^{2}+R^{2})^{3/2}}\).
Step 2: Compare
Comparing with \(\frac{xR^{2}}{(z^{2}+R^{2})^{3/2}}\), we get \(x=\frac{\mu_{0}I}{2}\).
Step 3: Check at the centre
At \(z=0\), \(B=\frac{\mu_{0}I}{2R}\), which is the known field at the centre of a loop, so this is consistent.
Step 4: Compare the options
This is option (C).
Final Answer:
The value of \(x\) is \(\frac{\mu_{0}I}{2}\). \[ \boxed{\text{(C) }\dfrac{\mu_{0}I}{2}} \]
The magnetic field on the axis of a circular loop of radius \(R\) carrying current \(I\) at distance \(z\) from its centre is \(B=\frac{\mu_{0}IR^{2}}{2(z^{2}+R^{2})^{3/2}}\).
Step 2: Compare
Comparing with \(\frac{xR^{2}}{(z^{2}+R^{2})^{3/2}}\), we get \(x=\frac{\mu_{0}I}{2}\).
Step 3: Check at the centre
At \(z=0\), \(B=\frac{\mu_{0}I}{2R}\), which is the known field at the centre of a loop, so this is consistent.
Step 4: Compare the options
This is option (C).
Final Answer:
The value of \(x\) is \(\frac{\mu_{0}I}{2}\). \[ \boxed{\text{(C) }\dfrac{\mu_{0}I}{2}} \]
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