NEET Exam  >  NEET Questions  >   A long solenoid of diameter 0.1 m has 2 x 10... Start Learning for Free
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)
    2
  • c)
    2
  • d)
    2
Correct answer is option 'C'. Can you explain this answer?
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.
Free Test
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).
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

Top Courses for NEET

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?
Question Description
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?.
Solutions 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? 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 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? defined & explained in the simplest way possible. Besides giving the explanation of 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 detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an ample number of questions to practice 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? tests, examples and also practice NEET tests.
Explore Courses for NEET exam

Top Courses for NEET

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev