NEET Exam > NEET Questions > A conducting circular loop is placed in a uni...
Start Learning for Free
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?
Most Upvoted Answer
A conducting circular loop is placed in a uniform magnetic field, B=0....
Community Answer
A conducting circular loop is placed in a uniform magnetic field, B=0....
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.
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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 detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup