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The electric current in a circular coil of two turns produced a magnetic induction of 0.2T at its centre. The coil is unwound and is rewound into a circular coil of four turns. The magnetic induction at the centre of the coil now is, in tesla (if same current flows in the coil)
- a)0.2
- b)0.4
- c)0.6
- d)0.8
Correct answer is option 'D'. Can you explain this answer?
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The electric current in a circular coil of two turns produced a magnet...
Given information:
- The circular coil has 2 turns initially.
- The magnetic induction at the center of the coil is 0.2T.
- The coil is then unwound and rewound into a circular coil with 4 turns.
- The current flowing through the coil remains the same.
To find:
The magnetic induction at the center of the coil with 4 turns.
Solution:
Step 1: Calculate the magnetic field produced by a single turn of the coil.
We know that the magnetic field produced by a single turn of a circular coil is given by the formula:
B = μ₀ * I * N / (2 * R)
Where:
- B is the magnetic induction
- μ₀ is the permeability of free space (constant)
- I is the current flowing through the coil
- N is the number of turns in the coil
- R is the radius of the coil
Step 2: Calculate the magnetic field produced by the initial coil with 2 turns.
Since the magnetic induction at the center of the initial coil is given as 0.2T, we can rearrange the formula to solve for the current:
I = (B * 2 * R) / (μ₀ * N)
Substituting the given values:
I = (0.2 * 2 * R) / (μ₀ * 2)
Step 3: Calculate the magnetic field produced by the coil with 4 turns.
Now that we know the current flowing through the coil, we can use the same formula to calculate the magnetic induction at the center of the coil with 4 turns:
B' = μ₀ * I' * N' / (2 * R')
Where:
- B' is the magnetic induction for the coil with 4 turns (to be determined)
- I' is the current flowing through the coil (same as initial current)
- N' is the number of turns in the new coil (4)
- R' is the radius of the new coil (same as initial radius)
Substituting the values:
B' = μ₀ * I * 4 / (2 * R)
Step 4: Simplify the expression and calculate the value of B'.
Since the radius of the initial coil and the new coil are the same, we can cancel out the 'R' terms in the equation:
B' = μ₀ * I * 4 / 2
Simplifying further:
B' = 2 * μ₀ * I
Step 5: Substitute the value of 'I' from Step 2.
Since the current flowing through the coil remains the same, we can substitute the value of 'I' calculated in Step 2:
B' = 2 * μ₀ * [(0.2 * 2 * R) / (μ₀ * 2)]
Simplifying further:
B' = (0.2 * 2 * R)
Step 6: Calculate the final value of B'.
Simplifying the expression:
B' = 0.4 * R
Therefore, the magnetic induction at the center of the coil with 4 turns is 0.4T.
Hence, the correct answer is option 'D' (0.8).
- The circular coil has 2 turns initially.
- The magnetic induction at the center of the coil is 0.2T.
- The coil is then unwound and rewound into a circular coil with 4 turns.
- The current flowing through the coil remains the same.
To find:
The magnetic induction at the center of the coil with 4 turns.
Solution:
Step 1: Calculate the magnetic field produced by a single turn of the coil.
We know that the magnetic field produced by a single turn of a circular coil is given by the formula:
B = μ₀ * I * N / (2 * R)
Where:
- B is the magnetic induction
- μ₀ is the permeability of free space (constant)
- I is the current flowing through the coil
- N is the number of turns in the coil
- R is the radius of the coil
Step 2: Calculate the magnetic field produced by the initial coil with 2 turns.
Since the magnetic induction at the center of the initial coil is given as 0.2T, we can rearrange the formula to solve for the current:
I = (B * 2 * R) / (μ₀ * N)
Substituting the given values:
I = (0.2 * 2 * R) / (μ₀ * 2)
Step 3: Calculate the magnetic field produced by the coil with 4 turns.
Now that we know the current flowing through the coil, we can use the same formula to calculate the magnetic induction at the center of the coil with 4 turns:
B' = μ₀ * I' * N' / (2 * R')
Where:
- B' is the magnetic induction for the coil with 4 turns (to be determined)
- I' is the current flowing through the coil (same as initial current)
- N' is the number of turns in the new coil (4)
- R' is the radius of the new coil (same as initial radius)
Substituting the values:
B' = μ₀ * I * 4 / (2 * R)
Step 4: Simplify the expression and calculate the value of B'.
Since the radius of the initial coil and the new coil are the same, we can cancel out the 'R' terms in the equation:
B' = μ₀ * I * 4 / 2
Simplifying further:
B' = 2 * μ₀ * I
Step 5: Substitute the value of 'I' from Step 2.
Since the current flowing through the coil remains the same, we can substitute the value of 'I' calculated in Step 2:
B' = 2 * μ₀ * [(0.2 * 2 * R) / (μ₀ * 2)]
Simplifying further:
B' = (0.2 * 2 * R)
Step 6: Calculate the final value of B'.
Simplifying the expression:
B' = 0.4 * R
Therefore, the magnetic induction at the center of the coil with 4 turns is 0.4T.
Hence, the correct answer is option 'D' (0.8).
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The electric current in a circular coil of two turns produced a magnetic induction of 0.2T at its centre. The coil is unwound and is rewound into a circular coil of four turns. The magnetic induction at the centre of the coil now is, in tesla (if same current flows in the coil)a)0.2b)0.4c)0.6d)0.8Correct answer is option 'D'. Can you explain this answer?
Question Description
The electric current in a circular coil of two turns produced a magnetic induction of 0.2T at its centre. The coil is unwound and is rewound into a circular coil of four turns. The magnetic induction at the centre of the coil now is, in tesla (if same current flows in the coil)a)0.2b)0.4c)0.6d)0.8Correct 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 The electric current in a circular coil of two turns produced a magnetic induction of 0.2T at its centre. The coil is unwound and is rewound into a circular coil of four turns. The magnetic induction at the centre of the coil now is, in tesla (if same current flows in the coil)a)0.2b)0.4c)0.6d)0.8Correct 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 The electric current in a circular coil of two turns produced a magnetic induction of 0.2T at its centre. The coil is unwound and is rewound into a circular coil of four turns. The magnetic induction at the centre of the coil now is, in tesla (if same current flows in the coil)a)0.2b)0.4c)0.6d)0.8Correct answer is option 'D'. Can you explain this answer?.
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Solutions for The electric current in a circular coil of two turns produced a magnetic induction of 0.2T at its centre. The coil is unwound and is rewound into a circular coil of four turns. The magnetic induction at the centre of the coil now is, in tesla (if same current flows in the coil)a)0.2b)0.4c)0.6d)0.8Correct 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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