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A circular coil of radius R having N number of turns carries a steady current I. The magnetic induction at the centre of the coil is 0.1 tesla. If the number of turns is doubled and the radius is halved, which one of the following will be the correct value for the magnetic induction at the centre of the coil?
  • a)
    0.05 tesla
  • b)
    0.2 tesla
  • c)
    0.4 tesla
  • d)
    0.8 tesla
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A circular coil of radius R having N number of turns carries a steady ...
Magnetic Induction B₁ = 0.1 tesla

n = No. of turns
a = Radius
I = current

β2 = 4 × 0.1= 0.4 tesla
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Most Upvoted Answer
A circular coil of radius R having N number of turns carries a steady ...
Given:
- Radius of the circular coil (initial) = R
- Number of turns in the coil (initial) = N
- Current in the coil = I
- Magnetic induction at the center of the coil (initial) = 0.1 Tesla

To find:
The value of magnetic induction at the center of the coil when the number of turns is doubled and the radius is halved.

Explanation:
1. Magnetic Field due to a Circular Coil:
The magnetic field at the center of a circular coil is given by the equation:

B = (μ₀ × N × I) / (2 × R)

Where:
- B is the magnetic field at the center of the coil
- μ₀ is the permeability of free space (= 4π × 10⁻⁷ Tesla meter/ampere)
- N is the number of turns in the coil
- I is the current in the coil
- R is the radius of the coil

2. Effect of Doubling the Number of Turns and Halving the Radius:
When the number of turns is doubled and the radius is halved, the new values become:
- Number of turns (final) = 2N
- Radius (final) = R/2

3. Calculating the Magnetic Induction at the Center of the Coil (final):
Using the formula for magnetic field:

B(final) = (μ₀ × N(final) × I) / (2 × R(final))

Substituting the values of N(final) and R(final):

B(final) = (μ₀ × 2N × I) / (2 × R/2)
= (μ₀ × N × I) / R
= B(initial) / R

Therefore, the magnetic induction at the center of the coil (final) is equal to the initial magnetic induction divided by the radius.

4. Calculation:
Given that the initial magnetic induction at the center of the coil is 0.1 Tesla, and the radius is halved, the final magnetic induction is:

B(final) = B(initial) / R
= 0.1 Tesla / (R/2)
= 0.1 Tesla × (2/R)
= 0.2 Tesla / R

Answer:
Therefore, the correct value for the magnetic induction at the center of the coil (final) is 0.2 Tesla / R. Thus, option B, 0.2 Tesla, is the correct answer.
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A circular coil of radius R having N number of turns carries a steady current I. The magnetic induction at the centre of the coil is 0.1 tesla. If the number of turns is doubled and the radius is halved, which one of the following will be the correct value for the magnetic induction at the centre of the coil?a)0.05 teslab)0.2 teslac)0.4 teslad)0.8 teslaCorrect answer is option 'C'. Can you explain this answer?
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A circular coil of radius R having N number of turns carries a steady current I. The magnetic induction at the centre of the coil is 0.1 tesla. If the number of turns is doubled and the radius is halved, which one of the following will be the correct value for the magnetic induction at the centre of the coil?a)0.05 teslab)0.2 teslac)0.4 teslad)0.8 teslaCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A circular coil of radius R having N number of turns carries a steady current I. The magnetic induction at the centre of the coil is 0.1 tesla. If the number of turns is doubled and the radius is halved, which one of the following will be the correct value for the magnetic induction at the centre of the coil?a)0.05 teslab)0.2 teslac)0.4 teslad)0.8 teslaCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular coil of radius R having N number of turns carries a steady current I. The magnetic induction at the centre of the coil is 0.1 tesla. If the number of turns is doubled and the radius is halved, which one of the following will be the correct value for the magnetic induction at the centre of the coil?a)0.05 teslab)0.2 teslac)0.4 teslad)0.8 teslaCorrect answer is option 'C'. Can you explain this answer?.
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