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A conducting circular loop is placed in a uniform magnetic field, B=0.025T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1mm per second . The induced emf when the radius is 2cm , is?
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Induced EMF in a Conducting Circular Loop
To determine the induced emf when the radius of a conducting circular loop is 2 cm, we can use Faraday's law of electromagnetic induction. According to this law, the induced emf in a circuit is equal to the rate of change of magnetic flux through the circuit.
Understanding the Problem
- A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T, with its plane perpendicular to the loop.
- The radius of the loop is shrinking at a constant rate of 1 mm per second.
Calculating the Magnetic Flux
The magnetic flux through a circular loop is given by the formula:
Φ = B * A * cos(θ)
Where:
- Φ is the magnetic flux
- B is the magnetic field strength
- A is the area of the loop
- θ is the angle between the magnetic field and the normal to the loop
In this case, the magnetic field is perpendicular to the loop, so the angle θ is 90 degrees and cos(θ) = 1. The formula simplifies to:
Φ = B * A
Calculating the Area of the Loop
The area of a circle is given by the formula:
A = π * r^2
Where:
- A is the area of the loop
- π is a mathematical constant (approximately 3.14159)
- r is the radius of the loop
Calculating the Rate of Change of Flux
Since the radius of the loop is shrinking at a constant rate of 1 mm per second, the rate of change of the radius (dr/dt) is equal to -0.1 cm/s. The rate of change of the flux (dΦ/dt) can be calculated using the chain rule of differentiation:
dΦ/dt = dB/dt * A + B * dA/dt
Since the magnetic field strength is constant, dB/dt = 0. Therefore, the equation simplifies to:
dΦ/dt = B * dA/dt
Calculating the Rate of Change of Area
The rate of change of the area (dA/dt) can be calculated using the chain rule of differentiation:
dA/dt = d(π * r^2)/dt
= 2πr * dr/dt
= 2π * 0.02 m * (-0.001 m/s)
= -0.00004π m^2/s
Calculating the Induced EMF
Now we can substitute the values into the equation for the rate of change of flux:
dΦ/dt = B * dA/dt
= (0.025 T) * (-0.00004π m^2/s)
≈ -7.854 x 10^-6 T*m^2/s
The induced emf (ε) is equal to the rate of change of flux:
ε = -dΦ/dt
= 7.854 x 10^-6 V
Therefore, the induced emf when the radius of the loop is 2 cm is approximately 7.854 microvolts.
To determine the induced emf when the radius of a conducting circular loop is 2 cm, we can use Faraday's law of electromagnetic induction. According to this law, the induced emf in a circuit is equal to the rate of change of magnetic flux through the circuit.
Understanding the Problem
- A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T, with its plane perpendicular to the loop.
- The radius of the loop is shrinking at a constant rate of 1 mm per second.
Calculating the Magnetic Flux
The magnetic flux through a circular loop is given by the formula:
Φ = B * A * cos(θ)
Where:
- Φ is the magnetic flux
- B is the magnetic field strength
- A is the area of the loop
- θ is the angle between the magnetic field and the normal to the loop
In this case, the magnetic field is perpendicular to the loop, so the angle θ is 90 degrees and cos(θ) = 1. The formula simplifies to:
Φ = B * A
Calculating the Area of the Loop
The area of a circle is given by the formula:
A = π * r^2
Where:
- A is the area of the loop
- π is a mathematical constant (approximately 3.14159)
- r is the radius of the loop
Calculating the Rate of Change of Flux
Since the radius of the loop is shrinking at a constant rate of 1 mm per second, the rate of change of the radius (dr/dt) is equal to -0.1 cm/s. The rate of change of the flux (dΦ/dt) can be calculated using the chain rule of differentiation:
dΦ/dt = dB/dt * A + B * dA/dt
Since the magnetic field strength is constant, dB/dt = 0. Therefore, the equation simplifies to:
dΦ/dt = B * dA/dt
Calculating the Rate of Change of Area
The rate of change of the area (dA/dt) can be calculated using the chain rule of differentiation:
dA/dt = d(π * r^2)/dt
= 2πr * dr/dt
= 2π * 0.02 m * (-0.001 m/s)
= -0.00004π m^2/s
Calculating the Induced EMF
Now we can substitute the values into the equation for the rate of change of flux:
dΦ/dt = B * dA/dt
= (0.025 T) * (-0.00004π m^2/s)
≈ -7.854 x 10^-6 T*m^2/s
The induced emf (ε) is equal to the rate of change of flux:
ε = -dΦ/dt
= 7.854 x 10^-6 V
Therefore, the induced emf when the radius of the loop is 2 cm is approximately 7.854 microvolts.
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A conducting circular loop is placed in a uniform magnetic field, B=0.025T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1mm per second . The induced emf when the radius is 2cm , is?
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A conducting circular loop is placed in a uniform magnetic field, B=0.025T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1mm per second . The induced emf when the radius is 2cm , is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A conducting circular loop is placed in a uniform magnetic field, B=0.025T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1mm per second . The induced emf when the radius is 2cm , is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A conducting circular loop is placed in a uniform magnetic field, B=0.025T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1mm per second . The induced emf when the radius is 2cm , is?.
A conducting circular loop is placed in a uniform magnetic field, B=0.025T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1mm per second . The induced emf when the radius is 2cm , is? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A conducting circular loop is placed in a uniform magnetic field, B=0.025T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1mm per second . The induced emf when the radius is 2cm , is? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A conducting circular loop is placed in a uniform magnetic field, B=0.025T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1mm per second . The induced emf when the radius is 2cm , is?.
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