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When a wheel with metal spokes 1.2m long is rotated about its axis in uniform magnetic field of flux density 5micro Tesla normal to the plane of the wheel an emf 0.01v is induced between the rim and the axle. Find rate of revolutions per second.?
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Given:
- Length of the metal spokes (r): 1.2 m
- Magnetic field flux density (B): 5 micro Tesla
- Induced electromotive force (emf): 0.01 V
To Find:
- Rate of revolutions per second (n)
Assumptions:
- The wheel is rotating about its axis in a uniform magnetic field.
- The magnetic field is normal to the plane of the wheel.
- The wheel is a perfect circle.
Formula:
The formula to calculate the induced emf is given by:
emf = B * A * ω
where,
emf = induced electromotive force (V)
B = magnetic field flux density (Tesla)
A = area of the loop (m²)
ω = angular velocity (rad/s)
The area of the loop is given by:
A = π * r²
where,
r = radius of the wheel (m)
The angular velocity can be related to the rate of revolutions per second as:
ω = 2π * n
where,
n = rate of revolutions per second
Solution:
1. Calculate the area of the loop:
A = π * (1.2 m)²
A = 4.5239 m²
2. Rearrange the formula for emf to solve for angular velocity:
ω = emf / (B * A)
= 0.01 V / (5 * 10^-6 Tesla * 4.5239 m²)
= 0.4416 rad/s
3. Use the relation between angular velocity and rate of revolutions per second to find n:
n = ω / (2π)
= 0.4416 rad/s / (2π)
≈ 0.0701 revolutions/s
Answer:
The rate of revolutions per second is approximately 0.0701 revolutions/s.
- Length of the metal spokes (r): 1.2 m
- Magnetic field flux density (B): 5 micro Tesla
- Induced electromotive force (emf): 0.01 V
To Find:
- Rate of revolutions per second (n)
Assumptions:
- The wheel is rotating about its axis in a uniform magnetic field.
- The magnetic field is normal to the plane of the wheel.
- The wheel is a perfect circle.
Formula:
The formula to calculate the induced emf is given by:
emf = B * A * ω
where,
emf = induced electromotive force (V)
B = magnetic field flux density (Tesla)
A = area of the loop (m²)
ω = angular velocity (rad/s)
The area of the loop is given by:
A = π * r²
where,
r = radius of the wheel (m)
The angular velocity can be related to the rate of revolutions per second as:
ω = 2π * n
where,
n = rate of revolutions per second
Solution:
1. Calculate the area of the loop:
A = π * (1.2 m)²
A = 4.5239 m²
2. Rearrange the formula for emf to solve for angular velocity:
ω = emf / (B * A)
= 0.01 V / (5 * 10^-6 Tesla * 4.5239 m²)
= 0.4416 rad/s
3. Use the relation between angular velocity and rate of revolutions per second to find n:
n = ω / (2π)
= 0.4416 rad/s / (2π)
≈ 0.0701 revolutions/s
Answer:
The rate of revolutions per second is approximately 0.0701 revolutions/s.
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When a wheel with metal spokes 1.2m long is rotated about its axis in uniform magnetic field of flux density 5micro Tesla normal to the plane of the wheel an emf 0.01v is induced between the rim and the axle. Find rate of revolutions per second.?
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When a wheel with metal spokes 1.2m long is rotated about its axis in uniform magnetic field of flux density 5micro Tesla normal to the plane of the wheel an emf 0.01v is induced between the rim and the axle. Find rate of revolutions per second.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about When a wheel with metal spokes 1.2m long is rotated about its axis in uniform magnetic field of flux density 5micro Tesla normal to the plane of the wheel an emf 0.01v is induced between the rim and the axle. Find rate of revolutions per second.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a wheel with metal spokes 1.2m long is rotated about its axis in uniform magnetic field of flux density 5micro Tesla normal to the plane of the wheel an emf 0.01v is induced between the rim and the axle. Find rate of revolutions per second.?.
When a wheel with metal spokes 1.2m long is rotated about its axis in uniform magnetic field of flux density 5micro Tesla normal to the plane of the wheel an emf 0.01v is induced between the rim and the axle. Find rate of revolutions per second.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about When a wheel with metal spokes 1.2m long is rotated about its axis in uniform magnetic field of flux density 5micro Tesla normal to the plane of the wheel an emf 0.01v is induced between the rim and the axle. Find rate of revolutions per second.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a wheel with metal spokes 1.2m long is rotated about its axis in uniform magnetic field of flux density 5micro Tesla normal to the plane of the wheel an emf 0.01v is induced between the rim and the axle. Find rate of revolutions per second.?.
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