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Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field B1, at its centre when a current (I) passes through it. The second wire is bent into a coil with three identical loops adjacent to each other and produces magnetic field B2 at the centre of the loops when current 1/3 passes through it. The ratio B1 : B2 is :
  • a)
    1 : 1
  • b)
    1 : 3
  • c)
    1 : 9
  • d)
    9 : 1
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Consider two thin identical conducting wires covered with very thin in...
Consider the following diagram,

The equation of magnetic field for loop wire is,

The equation of magnetic field for coiled wire is,

Taking ratio,

=1/3
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Most Upvoted Answer
Consider two thin identical conducting wires covered with very thin in...
Explanation:
To understand why the ratio of the magnetic fields is 1:3, let's consider the magnetic field produced by a single loop of wire and the magnetic field produced by three loops of wire.

Magnetic Field Produced by a Single Loop:
When a current I passes through a single loop of wire, it produces a magnetic field at its center. According to Ampere's Law, the magnetic field at the center of the loop can be calculated using the equation:

B1 = (μ0 * I) / (2 * R)

Where B1 is the magnetic field at the center of the loop, μ0 is the permeability of free space, I is the current passing through the loop, and R is the radius of the loop.

Magnetic Field Produced by Three Loops:
Now, let's consider three identical loops of wire placed adjacent to each other. If a current 1/3 passes through each loop, the total current passing through the three loops is 3 * (1/3) = 1.

According to Ampere's Law, the magnetic field at the center of the three loops can be calculated using the same equation as before:

B2 = (μ0 * (1/3)) / (2 * R)

Simplifying the equation, we get:

B2 = (μ0 / 6R)

Comparing the Ratios:
To find the ratio B1:B2, we can divide the two equations:

B1 / B2 = [(μ0 * I) / (2 * R)] / (μ0 / 6R)

Simplifying the equation, we get:

B1 / B2 = 6I / 2

B1 / B2 = 3I

Therefore, the ratio of B1 to B2 is 3:1 or 1:3.

Conclusion:
Hence, the correct answer is option B) 1:3. The magnetic field produced by three loops of wire with a current 1/3 passing through each loop is three times smaller than the magnetic field produced by a single loop with a current I passing through it.
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Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field B1, at its centre when a current (I) passes through it. The second wire is bent into a coil with three identical loops adjacent to each other and produces magnetic field B2 at the centre of the loops when current 1/3 passes through it. The ratio B1 : B2 is :a)1 : 1b)1 : 3c)1 : 9d)9 : 1Correct answer is option 'B'. Can you explain this answer?
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Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field B1, at its centre when a current (I) passes through it. The second wire is bent into a coil with three identical loops adjacent to each other and produces magnetic field B2 at the centre of the loops when current 1/3 passes through it. The ratio B1 : B2 is :a)1 : 1b)1 : 3c)1 : 9d)9 : 1Correct answer is option 'B'. 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 Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field B1, at its centre when a current (I) passes through it. The second wire is bent into a coil with three identical loops adjacent to each other and produces magnetic field B2 at the centre of the loops when current 1/3 passes through it. The ratio B1 : B2 is :a)1 : 1b)1 : 3c)1 : 9d)9 : 1Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field B1, at its centre when a current (I) passes through it. The second wire is bent into a coil with three identical loops adjacent to each other and produces magnetic field B2 at the centre of the loops when current 1/3 passes through it. The ratio B1 : B2 is :a)1 : 1b)1 : 3c)1 : 9d)9 : 1Correct answer is option 'B'. Can you explain this answer?.
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