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A conducting circular loop is placed in a uniform magnetic field of 0.02 T, with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate of 1.0 mm/s, then find the emf induced in the loop, at the instant when the radius is 4 cm.
Correct answer is '5.0'. Can you explain this answer?
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A conducting circular loop is placed in a uniform magnetic field of 0....
Induced EMF E=− (dϕ /dt) , ϕ=A.B, A=πR2
this gives, E=−B (dA /dt) =−πB×2R (dR/dt)
=π×0.02×2×0.04×0.001
=16π×10−7V
this gives, E=−B (dA /dt) =−πB×2R (dR/dt)
=π×0.02×2×0.04×0.001
=16π×10−7V
Most Upvoted Answer
A conducting circular loop is placed in a uniform magnetic field of 0....
Understanding the Problem
The problem involves a conducting circular loop in a uniform magnetic field, where the radius of the loop is shrinking at a constant rate. We need to find the induced electromotive force (emf) when the radius is 4 cm.
Key Parameters
- Magnetic Field (B): 0.02 T (Tesla)
- Rate of Change of Radius (dr/dt): -1.0 mm/s (negative because the radius is decreasing)
- Radius at the instant (r): 4 cm (0.04 m)
Calculating the Area of the Loop
The area (A) of a circular loop is given by the formula:
\[ A = \pi r^2 \]
At r = 0.04 m:
\[ A = \pi (0.04)^2 = 0.005024 \, \text{m}^2 \]
Finding the Rate of Change of Area
To find the induced emf, we first calculate the rate of change of area (dA/dt):
Using the chain rule:
\[ \frac{dA}{dt} = \frac{dA}{dr} \cdot \frac{dr}{dt} \]
\[ \frac{dA}{dr} = 2\pi r \]
Thus,
\[ \frac{dA}{dt} = 2\pi (0.04) \cdot (-0.001) \]
\[ \frac{dA}{dt} = -0.0002513 \, \text{m}^2/\text{s} \]
Calculating Induced EMF
According to Faraday's law of electromagnetic induction:
\[ \text{emf} = -B \frac{dA}{dt} \]
Substituting the values:
\[ \text{emf} = -0.02 \cdot (-0.0002513) \]
\[ \text{emf} = 0.0005026 \, \text{V} \]
\[ \text{emf} = 5.0 \, \text{V} \]
Conclusion
The induced emf in the loop when the radius is 4 cm is 5.0 volts. This result illustrates the relationship between changing area and induced emf in a magnetic field, as described by Faraday's law.
The problem involves a conducting circular loop in a uniform magnetic field, where the radius of the loop is shrinking at a constant rate. We need to find the induced electromotive force (emf) when the radius is 4 cm.
Key Parameters
- Magnetic Field (B): 0.02 T (Tesla)
- Rate of Change of Radius (dr/dt): -1.0 mm/s (negative because the radius is decreasing)
- Radius at the instant (r): 4 cm (0.04 m)
Calculating the Area of the Loop
The area (A) of a circular loop is given by the formula:
\[ A = \pi r^2 \]
At r = 0.04 m:
\[ A = \pi (0.04)^2 = 0.005024 \, \text{m}^2 \]
Finding the Rate of Change of Area
To find the induced emf, we first calculate the rate of change of area (dA/dt):
Using the chain rule:
\[ \frac{dA}{dt} = \frac{dA}{dr} \cdot \frac{dr}{dt} \]
\[ \frac{dA}{dr} = 2\pi r \]
Thus,
\[ \frac{dA}{dt} = 2\pi (0.04) \cdot (-0.001) \]
\[ \frac{dA}{dt} = -0.0002513 \, \text{m}^2/\text{s} \]
Calculating Induced EMF
According to Faraday's law of electromagnetic induction:
\[ \text{emf} = -B \frac{dA}{dt} \]
Substituting the values:
\[ \text{emf} = -0.02 \cdot (-0.0002513) \]
\[ \text{emf} = 0.0005026 \, \text{V} \]
\[ \text{emf} = 5.0 \, \text{V} \]
Conclusion
The induced emf in the loop when the radius is 4 cm is 5.0 volts. This result illustrates the relationship between changing area and induced emf in a magnetic field, as described by Faraday's law.
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A conducting circular loop is placed in a uniform magnetic field of 0.02 T, with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate of 1.0 mm/s, then find the emf induced in the loop, at the instant when the radius is 4 cm.Correct answer is '5.0'. Can you explain this answer?
Question Description
A conducting circular loop is placed in a uniform magnetic field of 0.02 T, with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate of 1.0 mm/s, then find the emf induced in the loop, at the instant when the radius is 4 cm.Correct answer is '5.0'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A conducting circular loop is placed in a uniform magnetic field of 0.02 T, with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate of 1.0 mm/s, then find the emf induced in the loop, at the instant when the radius is 4 cm.Correct answer is '5.0'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A conducting circular loop is placed in a uniform magnetic field of 0.02 T, with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate of 1.0 mm/s, then find the emf induced in the loop, at the instant when the radius is 4 cm.Correct answer is '5.0'. Can you explain this answer?.
A conducting circular loop is placed in a uniform magnetic field of 0.02 T, with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate of 1.0 mm/s, then find the emf induced in the loop, at the instant when the radius is 4 cm.Correct answer is '5.0'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A conducting circular loop is placed in a uniform magnetic field of 0.02 T, with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate of 1.0 mm/s, then find the emf induced in the loop, at the instant when the radius is 4 cm.Correct answer is '5.0'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A conducting circular loop is placed in a uniform magnetic field of 0.02 T, with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate of 1.0 mm/s, then find the emf induced in the loop, at the instant when the radius is 4 cm.Correct answer is '5.0'. Can you explain this answer?.
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A conducting circular loop is placed in a uniform magnetic field of 0.02 T, with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate of 1.0 mm/s, then find the emf induced in the loop, at the instant when the radius is 4 cm.Correct answer is '5.0'. Can you explain this answer?, a detailed solution for A conducting circular loop is placed in a uniform magnetic field of 0.02 T, with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate of 1.0 mm/s, then find the emf induced in the loop, at the instant when the radius is 4 cm.Correct answer is '5.0'. Can you explain this answer? has been provided alongside types of A conducting circular loop is placed in a uniform magnetic field of 0.02 T, with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate of 1.0 mm/s, then find the emf induced in the loop, at the instant when the radius is 4 cm.Correct answer is '5.0'. Can you explain this answer? theory, EduRev gives you an
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