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Magnetic field produced at the centre of a current carrying circular wire is :
- a)Directly proportional to the square of the radius of the circular wire
- b)Directly proportional to the radius of the circular wire
- c)Inversely proportional to the square of the radius of the circular wire
- d)none of these
Correct answer is option `D`. Can you explain this answer?
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- a)Directly proportional to the square of the radius of the circular wire
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Understanding the Magnetic Field at the Centre of a Circular Wire
The magnetic field produced at the centre of a current-carrying circular wire can be analyzed using Ampere's Law and the Biot-Savart Law.
Key Points:
- Magnetic Field Formula:
The magnetic field (B) at the centre of a circular loop of radius R carrying current I is given by the formula:
B = (μ₀ * I) / (4 * π * R)
- Dependence on Radius:
- The formula indicates that the magnetic field is inversely proportional to the radius (R) of the circular wire.
- As the radius increases, the magnetic field strength at the centre decreases. This is due to the distribution of current in a larger loop, which results in a weaker field at the centre.
Why Option D is Correct:
- None of the Given Options Fit:
- Option (a): Incorrect, as B is not directly proportional to R².
- Option (b): Incorrect, as B does not increase with R.
- Option (c): Incorrect, as B is not inversely proportional to R²; it is inversely proportional to R.
- Therefore, option (d) "none of these" is the correct answer.
Conclusion:
The magnetic field at the centre of a current-carrying circular wire does not fit the given proportionalities in the other options, confirming that the only accurate statement is option D. Understanding this relationship is crucial for fields like electromagnetism and circuit design.
The magnetic field produced at the centre of a current-carrying circular wire can be analyzed using Ampere's Law and the Biot-Savart Law.
Key Points:
- Magnetic Field Formula:
The magnetic field (B) at the centre of a circular loop of radius R carrying current I is given by the formula:
B = (μ₀ * I) / (4 * π * R)
- Dependence on Radius:
- The formula indicates that the magnetic field is inversely proportional to the radius (R) of the circular wire.
- As the radius increases, the magnetic field strength at the centre decreases. This is due to the distribution of current in a larger loop, which results in a weaker field at the centre.
Why Option D is Correct:
- None of the Given Options Fit:
- Option (a): Incorrect, as B is not directly proportional to R².
- Option (b): Incorrect, as B does not increase with R.
- Option (c): Incorrect, as B is not inversely proportional to R²; it is inversely proportional to R.
- Therefore, option (d) "none of these" is the correct answer.
Conclusion:
The magnetic field at the centre of a current-carrying circular wire does not fit the given proportionalities in the other options, confirming that the only accurate statement is option D. Understanding this relationship is crucial for fields like electromagnetism and circuit design.
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Magnetic field produced at the centre of a current carrying circular wire is :a)Directly proportional to the square of the radius of the circular wireb)Directly proportional to the radius of the circular wirec)Inversely proportional to the square of the radius of the circular wired)none of theseCorrect answer is option `D`. Can you explain this answer?
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