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A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop is
perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the
magnitude of induced emf will be maximum and minimum, respectively at
perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the
magnitude of induced emf will be maximum and minimum, respectively at
- a)5.0 s and 7.5 s
- b)5.0 s and 10.0s
- c)2.5 s and 7.5 s
- d)2.5 s and 5.0 s
Correct answer is option 'D'. Can you explain this answer?
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A planar loop of wire rotates in a uniform magnetic field. Initially a...
Understanding the Problem:
We have a planar loop of wire that is rotating in a uniform magnetic field. Initially, the plane of the loop is perpendicular to the magnetic field. The loop rotates with a period of 10 s about an axis in its plane. We need to determine the moments when the magnitude of the induced emf is maximum and minimum.
Key Concepts:
1. Faraday's Law of Electromagnetic Induction: It states that the induced electromotive force (emf) in a circuit is directly proportional to the rate of change of magnetic flux through the circuit.
2. Magnetic Flux: It is defined as the product of the magnetic field strength (B) and the area (A) perpendicular to the magnetic field.
3. Magnetic Flux through a Loop: When a loop of wire is placed in a magnetic field, the magnetic flux through the loop is given by the product of the magnetic field strength (B), the area (A) of the loop, and the cosine of the angle (θ) between the magnetic field and the normal to the loop.
Solution:
Given that the loop rotates with a period of 10 s, we can determine the angular velocity (ω) of the loop using the formula: ω = 2π / T, where T is the period.
Step 1: Determine the Angular Velocity
Given:
Period (T) = 10 s
Using the formula ω = 2π / T, we can calculate the angular velocity:
ω = 2π / 10
ω = π / 5 rad/s
Step 2: Determine the Angle of Rotation (θ)
Since the loop is initially perpendicular to the magnetic field, the angle of rotation (θ) will vary with time. We can express θ as a function of time (t) using the formula: θ = ωt.
Step 3: Determine the Magnetic Flux through the Loop
The magnetic flux through the loop is given by the formula: Φ = B * A * cos(θ).
Since the plane of the loop is initially perpendicular to the magnetic field, the magnetic flux through the loop will be maximum at t = 0 and minimum at t = T/2.
At t = 0, θ = 0, and cos(0) = 1. Therefore, the magnetic flux through the loop is maximum at t = 0.
At t = T/2, θ = ω * (T/2) = (π / 5) * (10 / 2) = π rad, and cos(π) = -1. Therefore, the magnetic flux through the loop is minimum at t = T/2.
Step 4: Determine the Induced emf
According to Faraday's Law of Electromagnetic Induction, the induced emf (ε) is given by the formula: ε = -dΦ/dt.
Since the magnetic flux through the loop is maximum at t = 0 and minimum at t = T/2, the rate of change of magnetic flux will be maximum at t = T/2 and minimum at t = 0.
Therefore, the magnitude of the induced emf will be maximum at t = T/2 and minimum at t = 0.
Conclusion:
We have a planar loop of wire that is rotating in a uniform magnetic field. Initially, the plane of the loop is perpendicular to the magnetic field. The loop rotates with a period of 10 s about an axis in its plane. We need to determine the moments when the magnitude of the induced emf is maximum and minimum.
Key Concepts:
1. Faraday's Law of Electromagnetic Induction: It states that the induced electromotive force (emf) in a circuit is directly proportional to the rate of change of magnetic flux through the circuit.
2. Magnetic Flux: It is defined as the product of the magnetic field strength (B) and the area (A) perpendicular to the magnetic field.
3. Magnetic Flux through a Loop: When a loop of wire is placed in a magnetic field, the magnetic flux through the loop is given by the product of the magnetic field strength (B), the area (A) of the loop, and the cosine of the angle (θ) between the magnetic field and the normal to the loop.
Solution:
Given that the loop rotates with a period of 10 s, we can determine the angular velocity (ω) of the loop using the formula: ω = 2π / T, where T is the period.
Step 1: Determine the Angular Velocity
Given:
Period (T) = 10 s
Using the formula ω = 2π / T, we can calculate the angular velocity:
ω = 2π / 10
ω = π / 5 rad/s
Step 2: Determine the Angle of Rotation (θ)
Since the loop is initially perpendicular to the magnetic field, the angle of rotation (θ) will vary with time. We can express θ as a function of time (t) using the formula: θ = ωt.
Step 3: Determine the Magnetic Flux through the Loop
The magnetic flux through the loop is given by the formula: Φ = B * A * cos(θ).
Since the plane of the loop is initially perpendicular to the magnetic field, the magnetic flux through the loop will be maximum at t = 0 and minimum at t = T/2.
At t = 0, θ = 0, and cos(0) = 1. Therefore, the magnetic flux through the loop is maximum at t = 0.
At t = T/2, θ = ω * (T/2) = (π / 5) * (10 / 2) = π rad, and cos(π) = -1. Therefore, the magnetic flux through the loop is minimum at t = T/2.
Step 4: Determine the Induced emf
According to Faraday's Law of Electromagnetic Induction, the induced emf (ε) is given by the formula: ε = -dΦ/dt.
Since the magnetic flux through the loop is maximum at t = 0 and minimum at t = T/2, the rate of change of magnetic flux will be maximum at t = T/2 and minimum at t = 0.
Therefore, the magnitude of the induced emf will be maximum at t = T/2 and minimum at t = 0.
Conclusion:
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A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop isperpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then themagnitude of induced emf will be maximum and minimum, respectively ata)5.0 s and 7.5 sb)5.0 s and 10.0sc)2.5 s and 7.5 sd)2.5 s and 5.0 sCorrect answer is option 'D'. Can you explain this answer?
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A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop isperpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then themagnitude of induced emf will be maximum and minimum, respectively ata)5.0 s and 7.5 sb)5.0 s and 10.0sc)2.5 s and 7.5 sd)2.5 s and 5.0 sCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop isperpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then themagnitude of induced emf will be maximum and minimum, respectively ata)5.0 s and 7.5 sb)5.0 s and 10.0sc)2.5 s and 7.5 sd)2.5 s and 5.0 sCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop isperpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then themagnitude of induced emf will be maximum and minimum, respectively ata)5.0 s and 7.5 sb)5.0 s and 10.0sc)2.5 s and 7.5 sd)2.5 s and 5.0 sCorrect answer is option 'D'. Can you explain this answer?.
A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop isperpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then themagnitude of induced emf will be maximum and minimum, respectively ata)5.0 s and 7.5 sb)5.0 s and 10.0sc)2.5 s and 7.5 sd)2.5 s and 5.0 sCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop isperpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then themagnitude of induced emf will be maximum and minimum, respectively ata)5.0 s and 7.5 sb)5.0 s and 10.0sc)2.5 s and 7.5 sd)2.5 s and 5.0 sCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop isperpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then themagnitude of induced emf will be maximum and minimum, respectively ata)5.0 s and 7.5 sb)5.0 s and 10.0sc)2.5 s and 7.5 sd)2.5 s and 5.0 sCorrect answer is option 'D'. Can you explain this answer?.
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