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A long solenoid of diameter 0.1 m has 2 x 104 turns per metre. At the centre of the solenoid, a 100-turn coil of radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid is decreased at a constant rate from + 2 A to - 2 A in 0.08 s. The emf (in mV) induced in the coil is
- a)π2
- b)2π2
- c)4π2
- d)8π2
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A long solenoid of diameter 0.1 m has 2 x 104 turns per metre. At the...
Concepts Used:
- Faraday's Law of Electromagnetic Induction
- Mutual Inductance
Explanation:
Step 1: Calculate the change in magnetic flux through the coil
- Initial current in the solenoid, I1 = 2 A
- Final current in the solenoid, I2 = -2 A
- Time taken for the current change, Δt = 0.08 s
- Rate of change of current, dI/dt = (I2 - I1) / Δt = (-2 - 2) / 0.08 = -50 A/s
- Magnetic field inside the solenoid, B = μ0 * n * I, where n is the number of turns per unit length
- Initial magnetic flux through the coil, Φ1 = π * (0.01)^2 * μ0 * 2 * 10^4
- Final magnetic flux through the coil, Φ2 = π * (0.01)^2 * μ0 * 2 * 10^4
- Change in magnetic flux, ΔΦ = Φ2 - Φ1
Step 2: Calculate the induced emf in the coil
- According to Faraday's Law of Electromagnetic Induction, the induced emf in the coil is given by:
emf = -N * dΦ/dt
- Here, N is the number of turns in the coil
- Since the coil is placed inside the solenoid, the magnetic flux change through the coil is due to the changing magnetic field of the solenoid
- Therefore, dΦ/dt = -M * dI/dt, where M is the mutual inductance between the solenoid and the coil
- Substituting the values, we get:
emf = N * M * 50
Step 3: Calculate the mutual inductance
- The mutual inductance between the solenoid and the coil is given by:
M = N * Φ / I
- Substituting the values, we get:
M = 100 * π * (0.01)^2 * μ0 * 2 * 10^4 / 2
Step 4: Calculate the induced emf in the coil
- Substituting the values of N, M, and dI/dt in the emf equation, we get:
emf = 100 * π * (0.01)^2 * μ0 * 2 * 10^4 / 2 * 50 = 4π^2
Therefore, the induced emf in the coil is 4π^2 mV. Option C is correct.
- Faraday's Law of Electromagnetic Induction
- Mutual Inductance
Explanation:
Step 1: Calculate the change in magnetic flux through the coil
- Initial current in the solenoid, I1 = 2 A
- Final current in the solenoid, I2 = -2 A
- Time taken for the current change, Δt = 0.08 s
- Rate of change of current, dI/dt = (I2 - I1) / Δt = (-2 - 2) / 0.08 = -50 A/s
- Magnetic field inside the solenoid, B = μ0 * n * I, where n is the number of turns per unit length
- Initial magnetic flux through the coil, Φ1 = π * (0.01)^2 * μ0 * 2 * 10^4
- Final magnetic flux through the coil, Φ2 = π * (0.01)^2 * μ0 * 2 * 10^4
- Change in magnetic flux, ΔΦ = Φ2 - Φ1
Step 2: Calculate the induced emf in the coil
- According to Faraday's Law of Electromagnetic Induction, the induced emf in the coil is given by:
emf = -N * dΦ/dt
- Here, N is the number of turns in the coil
- Since the coil is placed inside the solenoid, the magnetic flux change through the coil is due to the changing magnetic field of the solenoid
- Therefore, dΦ/dt = -M * dI/dt, where M is the mutual inductance between the solenoid and the coil
- Substituting the values, we get:
emf = N * M * 50
Step 3: Calculate the mutual inductance
- The mutual inductance between the solenoid and the coil is given by:
M = N * Φ / I
- Substituting the values, we get:
M = 100 * π * (0.01)^2 * μ0 * 2 * 10^4 / 2
Step 4: Calculate the induced emf in the coil
- Substituting the values of N, M, and dI/dt in the emf equation, we get:
emf = 100 * π * (0.01)^2 * μ0 * 2 * 10^4 / 2 * 50 = 4π^2
Therefore, the induced emf in the coil is 4π^2 mV. Option C is correct.
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Community Answer
A long solenoid of diameter 0.1 m has 2 x 104 turns per metre. At the...
Change in current ΔI = -2 - (+2) = -4 A.
Time taken Δt = 0.08 s. Therefore, induced emf is
So the correct choice is (C).
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A long solenoid of diameter 0.1 m has 2 x 104 turns per metre. At the centre of the solenoid, a 100-turn coil of radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid is decreased at a constant rate from + 2 A to - 2 A in 0.08 s. The emf (in mV) induced in the coil isa)π2b)2π2c)4π2d)8π2Correct answer is option 'C'. Can you explain this answer?
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A long solenoid of diameter 0.1 m has 2 x 104 turns per metre. At the centre of the solenoid, a 100-turn coil of radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid is decreased at a constant rate from + 2 A to - 2 A in 0.08 s. The emf (in mV) induced in the coil isa)π2b)2π2c)4π2d)8π2Correct answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A long solenoid of diameter 0.1 m has 2 x 104 turns per metre. At the centre of the solenoid, a 100-turn coil of radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid is decreased at a constant rate from + 2 A to - 2 A in 0.08 s. The emf (in mV) induced in the coil isa)π2b)2π2c)4π2d)8π2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A long solenoid of diameter 0.1 m has 2 x 104 turns per metre. At the centre of the solenoid, a 100-turn coil of radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid is decreased at a constant rate from + 2 A to - 2 A in 0.08 s. The emf (in mV) induced in the coil isa)π2b)2π2c)4π2d)8π2Correct answer is option 'C'. Can you explain this answer?.
A long solenoid of diameter 0.1 m has 2 x 104 turns per metre. At the centre of the solenoid, a 100-turn coil of radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid is decreased at a constant rate from + 2 A to - 2 A in 0.08 s. The emf (in mV) induced in the coil isa)π2b)2π2c)4π2d)8π2Correct answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A long solenoid of diameter 0.1 m has 2 x 104 turns per metre. At the centre of the solenoid, a 100-turn coil of radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid is decreased at a constant rate from + 2 A to - 2 A in 0.08 s. The emf (in mV) induced in the coil isa)π2b)2π2c)4π2d)8π2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A long solenoid of diameter 0.1 m has 2 x 104 turns per metre. At the centre of the solenoid, a 100-turn coil of radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid is decreased at a constant rate from + 2 A to - 2 A in 0.08 s. The emf (in mV) induced in the coil isa)π2b)2π2c)4π2d)8π2Correct answer is option 'C'. Can you explain this answer?.
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