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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 Data:
- Number of turns in the initial coil (N₁) = 2
- Magnetic induction at the center of the initial coil (B₁) = 0.2T
- Number of turns in the final coil (N₂) = 4
- Magnetic induction at the center of the final coil (B₂) = ?
Solution:
- The magnetic induction at the center of a circular coil is given by the formula:
\[ B = \frac{{\mu \cdot N \cdot I}}{{2 \cdot r}} \]
where,
B = Magnetic induction
μ = Permeability of the medium
N = Number of turns in the coil
I = Current flowing through the coil
r = Radius of the coil
Step 1: Calculating the magnetic induction for the initial coil:
Given, N₁ = 2, B₁ = 0.2T
Using the formula:
\[ 0.2 = \frac{{\mu \cdot 2 \cdot I}}{{2 \cdot r}} \]
\[ 0.2 = \frac{{\mu \cdot I}}{{r}} \]
\[ r = \frac{{0.2 \cdot \mu}}{{I}} \]
Step 2: Calculating the magnetic induction for the final coil:
For the final coil with N₂ = 4 turns, the radius will remain the same as the initial coil. So, using the formula for the final coil:
\[ B₂ = \frac{{\mu \cdot 4 \cdot I}}{{2 \cdot r}} \]
\[ B₂ = \frac{{\mu \cdot 4 \cdot I}}{{2 \cdot (\frac{{0.2 \cdot \mu}}{{I}})}} \]
\[ B₂ = \frac{{4}}{{2}} \cdot \frac{1}{{0.2}} \cdot I \]
\[ B₂ = 2 \cdot 5 \cdot I \]
\[ B₂ = 10 \cdot I = 10 \times 0.2 = 2T \]
Therefore, the magnetic induction at the center of the coil with four turns is 0.8T. So, the correct answer is option D (0.8).
- Number of turns in the initial coil (N₁) = 2
- Magnetic induction at the center of the initial coil (B₁) = 0.2T
- Number of turns in the final coil (N₂) = 4
- Magnetic induction at the center of the final coil (B₂) = ?
Solution:
- The magnetic induction at the center of a circular coil is given by the formula:
\[ B = \frac{{\mu \cdot N \cdot I}}{{2 \cdot r}} \]
where,
B = Magnetic induction
μ = Permeability of the medium
N = Number of turns in the coil
I = Current flowing through the coil
r = Radius of the coil
Step 1: Calculating the magnetic induction for the initial coil:
Given, N₁ = 2, B₁ = 0.2T
Using the formula:
\[ 0.2 = \frac{{\mu \cdot 2 \cdot I}}{{2 \cdot r}} \]
\[ 0.2 = \frac{{\mu \cdot I}}{{r}} \]
\[ r = \frac{{0.2 \cdot \mu}}{{I}} \]
Step 2: Calculating the magnetic induction for the final coil:
For the final coil with N₂ = 4 turns, the radius will remain the same as the initial coil. So, using the formula for the final coil:
\[ B₂ = \frac{{\mu \cdot 4 \cdot I}}{{2 \cdot r}} \]
\[ B₂ = \frac{{\mu \cdot 4 \cdot I}}{{2 \cdot (\frac{{0.2 \cdot \mu}}{{I}})}} \]
\[ B₂ = \frac{{4}}{{2}} \cdot \frac{1}{{0.2}} \cdot I \]
\[ B₂ = 2 \cdot 5 \cdot I \]
\[ B₂ = 10 \cdot I = 10 \times 0.2 = 2T \]
Therefore, the magnetic induction at the center of the coil with four turns is 0.8T. So, 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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