A wire carries a current. Maintaining the samecurrent it is bent first to form a circular plane coil ofone turn which produces a magnetic field B at thecentre of the coil. The same length is now bentmore sharply to give a double loop of smaller radius.The magnetic field at the centre of the double loop,caused by the same current is [2002]a)4Bb)B/4c)B/2d)2BCorrect answer is option 'A'. Can you explain this answer?

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A wire carries a current. Maintaining the samecurrent it is bent first to form a circular plane coil ofone turn which produces a magnetic field B at thecentre of the coil. The same length is now bentmore sharply to give a double loop of smaller radius.The magnetic field at the centre of the double loop,caused by the same current is [2002]

a)
4B
b)
B/4
c)
B/2
d)
2B

Correct answer is option 'A'. Can you explain this answer?

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A wire carries a current. Maintaining the samecurrent it is bent first...

Let I be current and l be the length of the wire.
For Ist case :

where
2πr = l and n = 1

For IInd Case :

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A wire carries a current. Maintaining the samecurrent it is bent first...

Principle:
The magnetic field at the center of a circular coil carrying current is given by the equation: B = μ₀I/(2R), where B is the magnetic field, μ₀ is the permeability of free space, I is the current, and R is the radius of the coil.

Explanation:
When the wire is bent to form a circular plane coil of one turn, the radius of the coil can be denoted as R₁. The magnetic field at the center of the coil is given by B₁ = μ₀I/(2R₁).

Now, the same length of wire is bent more sharply to form a double loop of smaller radius. Let's denote the radius of the double loop as R₂. Since the length of the wire is the same, the circumference of the double loop will be smaller than that of the circular coil. Therefore, the radius of the double loop will be smaller than R₁.

Comparison between the circular coil and the double loop:
To compare the magnetic fields at the center of the circular coil and the double loop, we can use the equation B = μ₀I/(2R).

Considering the circular coil:
B₁ = μ₀I/(2R₁)

Considering the double loop:
B₂ = μ₀I/(2R₂)

Since R₂ < r₁="" (the="" radius="" of="" the="" double="" loop="" is="" smaller="" than="" the="" radius="" of="" the="" circular="" coil),="" we="" can="" conclude="" that="" r₁/r₂="" /> 1.

Comparing B₁ and B₂:
To compare B₁ and B₂, we can divide the equation for B₂ by the equation for B₁:
B₂/B₁ = (μ₀I/(2R₂)) / (μ₀I/(2R₁))
B₂/B₁ = R₁/R₂ > 1

Therefore, the magnetic field at the center of the double loop (B₂) is greater than the magnetic field at the center of the circular coil (B₁).

Conclusion:
The magnetic field at the center of the double loop, caused by the same current, is greater than the magnetic field at the center of the circular coil. Therefore, the correct answer is option 'A': 4B.

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A wire carries a current. Maintaining the samecurrent it is bent first to form a circular plane coil ofone turn which produces a magnetic field B at thecentre of the coil. The same length is now bentmore sharply to give a double loop of smaller radius.The magnetic field at the centre of the double loop,caused by the same current is [2002]a)4Bb)B/4c)B/2d)2BCorrect answer is option 'A'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A wire carries a current. Maintaining the samecurrent it is bent first to form a circular plane coil ofone turn which produces a magnetic field B at thecentre of the coil. The same length is now bentmore sharply to give a double loop of smaller radius.The magnetic field at the centre of the double loop,caused by the same current is [2002]a)4Bb)B/4c)B/2d)2BCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wire carries a current. Maintaining the samecurrent it is bent first to form a circular plane coil ofone turn which produces a magnetic field B at thecentre of the coil. The same length is now bentmore sharply to give a double loop of smaller radius.The magnetic field at the centre of the double loop,caused by the same current is [2002]a)4Bb)B/4c)B/2d)2BCorrect answer is option 'A'. Can you explain this answer?.

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