Question:
The magnetic field at the centre of a circular coil of radius $r$ carrying a current $I$ is proportional to
The magnetic field at the centre of a circular coil of radius $r$ carrying a current $I$ is proportional to
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Remember that for circular coils, the magnetic field strength decreases as the radius increases, and it directly depends on the current flowing through the coil.
Updated On: Jun 3, 2026
- $I / r$
- $I r$
- $I / r^2$
- $I r^2$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
The magnetic field at the center of a circular coil can be calculated using Ampère's circuital law or Biot-Savart law. For a circular coil, the magnetic field is directly proportional to the current and inversely proportional to the radius of the coil.
Step 2: Meaning
This means that if we increase the current flowing through the coil, the magnetic field at its center will also increase proportionally. Conversely, increasing the radius of the coil will decrease the magnetic field at its center due to a larger distance from each infinitesimal segment contributing to the overall field.
Step 3: Analysis
To derive the relationship between the magnetic field \( B \) at the center of a circular coil and the given parameters, we can use the formula for the magnetic field at the center of a circular loop: \[B = \frac{\mu_0 I}{2r}\] where: \( B \) is the magnetic field, \( \mu_0 \) is the permeability of free space (a constant), \( I \) is the current in the coil, \( r \) is the radius of the circular coil. From this formula, we can see that \( B \) is directly proportional to \( I \) and inversely proportional to \( r \). This matches option A: \( I / r \).
Step 4: Conclusion
The magnetic field at the center of a circular coil is indeed proportional to the current divided by the radius.
Final Answer: (A)
The magnetic field at the center of a circular coil can be calculated using Ampère's circuital law or Biot-Savart law. For a circular coil, the magnetic field is directly proportional to the current and inversely proportional to the radius of the coil.
Step 2: Meaning
This means that if we increase the current flowing through the coil, the magnetic field at its center will also increase proportionally. Conversely, increasing the radius of the coil will decrease the magnetic field at its center due to a larger distance from each infinitesimal segment contributing to the overall field.
Step 3: Analysis
To derive the relationship between the magnetic field \( B \) at the center of a circular coil and the given parameters, we can use the formula for the magnetic field at the center of a circular loop: \[B = \frac{\mu_0 I}{2r}\] where: \( B \) is the magnetic field, \( \mu_0 \) is the permeability of free space (a constant), \( I \) is the current in the coil, \( r \) is the radius of the circular coil. From this formula, we can see that \( B \) is directly proportional to \( I \) and inversely proportional to \( r \). This matches option A: \( I / r \).
Step 4: Conclusion
The magnetic field at the center of a circular coil is indeed proportional to the current divided by the radius.
Final Answer: (A)
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