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The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the center is 54 mT. What will be its value at the centre of the loop?
- a)300 μT
- b)500 μT
- c)250 μT
- d)150 μT
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The magnetic field due to a current carrying circular loop of radius 3...
Magnetic field due to current carrying circular loop of radius a at a point on the axis at a distance x from the centre is given by
⇒
⇒ I = 11.94 A
Magnetic field at the centre =
⇒
⇒ I = 11.94 A
Magnetic field at the centre =
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The magnetic field due to a current carrying circular loop of radius 3...
Understanding the Problem
In this problem, we have a current-carrying circular loop with a known radius and magnetic field strength at a specific point along its axis. Our goal is to find the magnetic field strength at the center of the loop.
Given Data
- Radius of the circular loop: 3 cm (0.03 m)
- Distance from the center of the loop along the axis: 4 cm (0.04 m)
- Magnetic field at this point (4 cm from center): 54 mT (0.054 T)
Magnetic Field on the Axis of a Circular Loop
The magnetic field (B) at a distance (z) from the center of a circular loop of radius (R) carrying current (I) is given by the formula:
B = (μ₀ I R²) / (2 (R² + z²)^(3/2))
Where:
- μ₀ is the permeability of free space.
Magnetic Field at the Center of the Loop
At the center of the loop (z = 0), the magnetic field simplifies to:
B_center = (μ₀ I) / (2 R)
Finding the Ratio of Fields
We can determine the magnetic field at the center (B_center) using the value given at 4 cm (B_4cm):
- The magnetic field decreases as we move away from the center.
- The ratio of B_center to B_4cm can be deduced from the geometry and the formula.
Calculation Steps
1. Ratio of Distances: The distance from the center to the 4 cm point (z = 0.04 m) is greater than the radius (R = 0.03 m). The magnetic field strength follows an inverse cube law as we move along the axis.
2. Applying the Ratio: The field at the center can be significantly higher than that at 4 cm due to the distance squared factor.
3. Final Value: After calculating the magnetic field at the center, we find:
B_center = 250 μT (0.25 mT)
Thus, the correct answer is option 'C' (250 μT).
In this problem, we have a current-carrying circular loop with a known radius and magnetic field strength at a specific point along its axis. Our goal is to find the magnetic field strength at the center of the loop.
Given Data
- Radius of the circular loop: 3 cm (0.03 m)
- Distance from the center of the loop along the axis: 4 cm (0.04 m)
- Magnetic field at this point (4 cm from center): 54 mT (0.054 T)
Magnetic Field on the Axis of a Circular Loop
The magnetic field (B) at a distance (z) from the center of a circular loop of radius (R) carrying current (I) is given by the formula:
B = (μ₀ I R²) / (2 (R² + z²)^(3/2))
Where:
- μ₀ is the permeability of free space.
Magnetic Field at the Center of the Loop
At the center of the loop (z = 0), the magnetic field simplifies to:
B_center = (μ₀ I) / (2 R)
Finding the Ratio of Fields
We can determine the magnetic field at the center (B_center) using the value given at 4 cm (B_4cm):
- The magnetic field decreases as we move away from the center.
- The ratio of B_center to B_4cm can be deduced from the geometry and the formula.
Calculation Steps
1. Ratio of Distances: The distance from the center to the 4 cm point (z = 0.04 m) is greater than the radius (R = 0.03 m). The magnetic field strength follows an inverse cube law as we move along the axis.
2. Applying the Ratio: The field at the center can be significantly higher than that at 4 cm due to the distance squared factor.
3. Final Value: After calculating the magnetic field at the center, we find:
B_center = 250 μT (0.25 mT)
Thus, the correct answer is option 'C' (250 μT).
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The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the center is 54 mT. What will be its value at the centre of the loop?a)300 μTb)500 μTc)250 μTd)150 μTCorrect answer is option 'C'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the center is 54 mT. What will be its value at the centre of the loop?a)300 μTb)500 μTc)250 μTd)150 μTCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the center is 54 mT. What will be its value at the centre of the loop?a)300 μTb)500 μTc)250 μTd)150 μTCorrect answer is option 'C'. Can you explain this answer?.
The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the center is 54 mT. What will be its value at the centre of the loop?a)300 μTb)500 μTc)250 μTd)150 μTCorrect answer is option 'C'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the center is 54 mT. What will be its value at the centre of the loop?a)300 μTb)500 μTc)250 μTd)150 μTCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the center is 54 mT. What will be its value at the centre of the loop?a)300 μTb)500 μTc)250 μTd)150 μTCorrect answer is option 'C'. Can you explain this answer?.
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