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A ring of resistance 10 Ω radius 10 cm and 100 turns is rotated at a rate of 100 rev/sec about its diameter is perpendicular to a uniform field of induction 10mT. The amplitude of the current in the loop will be nearly?
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A ring of resistance 10 Ω radius 10 cm and 100 turns is rotated at a r...
Given data:
Resistance of the ring (R) = 10 Ω
Radius of the ring (r) = 10 cm = 0.1 m
Number of turns in the ring (N) = 100
Rate of rotation (ω) = 100 rev/sec
Magnetic field strength (B) = 10 mT = 0.01 T
Formula:
The induced emf (ε) in a rotating loop is given by Faraday's law of electromagnetic induction:
ε = -N(dΦ/dt)
The magnetic flux (Φ) through a loop is given by:
Φ = B*A*cos(θ)
Where A is the area of the loop and θ is the angle between the normal to the loop and the magnetic field.
Calculating the area of the loop:
The area of the loop can be calculated using the formula:
A = π*r^2
Substituting the given values:
A = π*(0.1)^2
A = 0.01π m^2
Calculating the rate of change of flux:
The rate of change of flux can be calculated using the formula:
(dΦ/dt) = d(B*A*cos(θ))/dt = B*d(A*cos(θ))/dt
Since the loop is rotating about its diameter, the angle θ between the normal to the loop and the magnetic field will be changing sinusoidally with time.
Assuming the loop is initially perpendicular to the magnetic field (θ = 0), the angle θ can be given by:
θ = ω*t
Where ω is the angular velocity and t is the time.
Substituting the values:
(dΦ/dt) = B*d(A*cos(ω*t))/dt = -B*A*ω*sin(ω*t)
Calculating the induced emf:
Using Faraday's law, the induced emf can be calculated as:
ε = -N*(dΦ/dt) = N*B*A*ω*sin(ω*t)
Substituting the given values:
ε = 100*0.01*π*0.1*0.01*100*sin(100*2π*t)
Simplifying the equation:
ε = 0.1π*sin(200πt)
Calculating the amplitude of the current:
The amplitude of the current (I) can be calculated using Ohm's law:
I = ε/R
Substituting the values:
I = 0.1π*sin(200πt)/10
I = 0.01π*sin(200πt)
Therefore, the amplitude of the current in the loop is 0.01π Amps.
Resistance of the ring (R) = 10 Ω
Radius of the ring (r) = 10 cm = 0.1 m
Number of turns in the ring (N) = 100
Rate of rotation (ω) = 100 rev/sec
Magnetic field strength (B) = 10 mT = 0.01 T
Formula:
The induced emf (ε) in a rotating loop is given by Faraday's law of electromagnetic induction:
ε = -N(dΦ/dt)
The magnetic flux (Φ) through a loop is given by:
Φ = B*A*cos(θ)
Where A is the area of the loop and θ is the angle between the normal to the loop and the magnetic field.
Calculating the area of the loop:
The area of the loop can be calculated using the formula:
A = π*r^2
Substituting the given values:
A = π*(0.1)^2
A = 0.01π m^2
Calculating the rate of change of flux:
The rate of change of flux can be calculated using the formula:
(dΦ/dt) = d(B*A*cos(θ))/dt = B*d(A*cos(θ))/dt
Since the loop is rotating about its diameter, the angle θ between the normal to the loop and the magnetic field will be changing sinusoidally with time.
Assuming the loop is initially perpendicular to the magnetic field (θ = 0), the angle θ can be given by:
θ = ω*t
Where ω is the angular velocity and t is the time.
Substituting the values:
(dΦ/dt) = B*d(A*cos(ω*t))/dt = -B*A*ω*sin(ω*t)
Calculating the induced emf:
Using Faraday's law, the induced emf can be calculated as:
ε = -N*(dΦ/dt) = N*B*A*ω*sin(ω*t)
Substituting the given values:
ε = 100*0.01*π*0.1*0.01*100*sin(100*2π*t)
Simplifying the equation:
ε = 0.1π*sin(200πt)
Calculating the amplitude of the current:
The amplitude of the current (I) can be calculated using Ohm's law:
I = ε/R
Substituting the values:
I = 0.1π*sin(200πt)/10
I = 0.01π*sin(200πt)
Therefore, the amplitude of the current in the loop is 0.01π Amps.
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A ring of resistance 10 Ω radius 10 cm and 100 turns is rotated at a rate of 100 rev/sec about its diameter is perpendicular to a uniform field of induction 10mT. The amplitude of the current in the loop will be nearly?
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A ring of resistance 10 Ω radius 10 cm and 100 turns is rotated at a rate of 100 rev/sec about its diameter is perpendicular to a uniform field of induction 10mT. The amplitude of the current in the loop will be nearly? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A ring of resistance 10 Ω radius 10 cm and 100 turns is rotated at a rate of 100 rev/sec about its diameter is perpendicular to a uniform field of induction 10mT. The amplitude of the current in the loop will be nearly? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ring of resistance 10 Ω radius 10 cm and 100 turns is rotated at a rate of 100 rev/sec about its diameter is perpendicular to a uniform field of induction 10mT. The amplitude of the current in the loop will be nearly?.
A ring of resistance 10 Ω radius 10 cm and 100 turns is rotated at a rate of 100 rev/sec about its diameter is perpendicular to a uniform field of induction 10mT. The amplitude of the current in the loop will be nearly? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A ring of resistance 10 Ω radius 10 cm and 100 turns is rotated at a rate of 100 rev/sec about its diameter is perpendicular to a uniform field of induction 10mT. The amplitude of the current in the loop will be nearly? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ring of resistance 10 Ω radius 10 cm and 100 turns is rotated at a rate of 100 rev/sec about its diameter is perpendicular to a uniform field of induction 10mT. The amplitude of the current in the loop will be nearly?.
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