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A conducting circular loop is placed in a uniform magnetic field 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm s−1. The induced emf in the loop, when the radius is 2 cm, is
- a)4.8π μV
- b)0.8π μV
- c)1.6π μV
- d)3.2π μV
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A conducting circular loop is placed in a uniform magnetic field 0.04...
Given information:
- Magnetic field strength (B) = 0.04 T
- Rate of change of radius (dr/dt) = -2 mm/s = -0.002 m/s
Concept:
When a conducting loop is placed in a changing magnetic field, an electromotive force (emf) is induced in the loop. This is known as electromagnetic induction. The magnitude of the induced emf can be calculated using Faraday's law of electromagnetic induction.
Calculation:
The induced emf in the loop is given by the equation:
emf = -N * dΦ/dt
Where,
N = number of turns in the loop
dΦ/dt = rate of change of magnetic flux through the loop
In this case, the loop is a conducting circular loop with a changing radius. The magnetic flux through the loop is given by the equation:
Φ = B * A
Where,
B = magnetic field strength
A = area of the loop
As the loop's radius is shrinking, the area of the loop is also changing. The area of the loop is given by the equation:
A = π * r^2
Where,
r = radius of the loop
Now, let's calculate the values step by step.
Step 1:
Calculate the area of the loop when the radius is 2 cm (0.02 m):
A = π * (0.02)^2 = 0.0012566 m^2
Step 2:
Calculate the rate of change of magnetic flux through the loop:
dΦ/dt = B * dA/dt
Since the magnetic field is uniform and perpendicular to the loop, the rate of change of magnetic flux is equal to the rate of change of the area of the loop:
dΦ/dt = B * dA/dt = B * 2πr * (dr/dt)
Substituting the given values:
dΦ/dt = 0.04 * 2π * 0.02 * (-0.002) = -0.000502 m^2/s
Step 3:
Calculate the induced emf in the loop:
emf = -N * dΦ/dt
Since the number of turns (N) is not given, we can assume it to be 1 for simplicity:
emf = -1 * (-0.000502) = 0.000502 V
Finally, convert the emf into microvolts:
emf = 0.000502 * 10^6 = 502 μV
Therefore, the induced emf in the loop, when the radius is 2 cm, is approximately 502 μV. Since none of the given options match this value, there seems to be an error in the question or options provided.
- Magnetic field strength (B) = 0.04 T
- Rate of change of radius (dr/dt) = -2 mm/s = -0.002 m/s
Concept:
When a conducting loop is placed in a changing magnetic field, an electromotive force (emf) is induced in the loop. This is known as electromagnetic induction. The magnitude of the induced emf can be calculated using Faraday's law of electromagnetic induction.
Calculation:
The induced emf in the loop is given by the equation:
emf = -N * dΦ/dt
Where,
N = number of turns in the loop
dΦ/dt = rate of change of magnetic flux through the loop
In this case, the loop is a conducting circular loop with a changing radius. The magnetic flux through the loop is given by the equation:
Φ = B * A
Where,
B = magnetic field strength
A = area of the loop
As the loop's radius is shrinking, the area of the loop is also changing. The area of the loop is given by the equation:
A = π * r^2
Where,
r = radius of the loop
Now, let's calculate the values step by step.
Step 1:
Calculate the area of the loop when the radius is 2 cm (0.02 m):
A = π * (0.02)^2 = 0.0012566 m^2
Step 2:
Calculate the rate of change of magnetic flux through the loop:
dΦ/dt = B * dA/dt
Since the magnetic field is uniform and perpendicular to the loop, the rate of change of magnetic flux is equal to the rate of change of the area of the loop:
dΦ/dt = B * dA/dt = B * 2πr * (dr/dt)
Substituting the given values:
dΦ/dt = 0.04 * 2π * 0.02 * (-0.002) = -0.000502 m^2/s
Step 3:
Calculate the induced emf in the loop:
emf = -N * dΦ/dt
Since the number of turns (N) is not given, we can assume it to be 1 for simplicity:
emf = -1 * (-0.000502) = 0.000502 V
Finally, convert the emf into microvolts:
emf = 0.000502 * 10^6 = 502 μV
Therefore, the induced emf in the loop, when the radius is 2 cm, is approximately 502 μV. Since none of the given options match this value, there seems to be an error in the question or options provided.
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A conducting circular loop is placed in a uniform magnetic field 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm s−1. The induced emf in the loop, when the radius is 2 cm, isa)4.8π μVb)0.8π μVc)1.6π μVd)3.2π μVCorrect answer is option 'D'. Can you explain this answer?
Question Description
A conducting circular loop is placed in a uniform magnetic field 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm s−1. The induced emf in the loop, when the radius is 2 cm, isa)4.8π μVb)0.8π μVc)1.6π μVd)3.2π μVCorrect 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 conducting circular loop is placed in a uniform magnetic field 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm s−1. The induced emf in the loop, when the radius is 2 cm, isa)4.8π μVb)0.8π μVc)1.6π μVd)3.2π μVCorrect 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 conducting circular loop is placed in a uniform magnetic field 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm s−1. The induced emf in the loop, when the radius is 2 cm, isa)4.8π μVb)0.8π μVc)1.6π μVd)3.2π μVCorrect answer is option 'D'. Can you explain this answer?.
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Solutions for A conducting circular loop is placed in a uniform magnetic field 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm s−1. The induced emf in the loop, when the radius is 2 cm, isa)4.8π μVb)0.8π μVc)1.6π μVd)3.2π μVCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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