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A conducting square loop pqrs of zero resistance but containing an inductor l is placed near a long wire carrying current isin(omegat) as shown in figure. Find the peak value of induced current in the loop?
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A conducting square loop pqrs of zero resistance but containing an ind...
Given:
- A conducting square loop PQRS of zero resistance is placed near a long wire carrying current I*sin(ωt).
- The square loop contains an inductor L.
To find:
The peak value of induced current in the loop.
Explanation:
1. Faraday's Law of Electromagnetic Induction:
According to Faraday's law of electromagnetic induction, an induced emf is produced in a closed loop when the magnetic flux passing through the loop changes. The induced emf is given by:
ε = -dΦ/dt,
where ε is the induced emf and dΦ/dt is the rate of change of magnetic flux.
2. Calculation of Magnetic Flux:
The magnetic flux passing through the square loop can be calculated as the product of magnetic field and the area of the loop. The magnetic field produced by the long wire carrying current I*sin(ωt) at a point P on the loop can be given by Ampere's Law:
B = (μ0*I)/(2πr),
where B is the magnetic field, μ0 is the permeability of free space, I is the current, and r is the distance between the long wire and point P on the loop.
3. Calculation of Induced EMF:
The induced emf in the loop can be calculated as the rate of change of magnetic flux. Since the magnetic field produced by the long wire is constant, the rate of change of magnetic flux is zero. Hence, the induced emf is zero.
4. Calculation of Induced Current:
Since the induced emf is zero, there is no current induced in the loop.
Conclusion:
The peak value of induced current in the loop is zero.
- A conducting square loop PQRS of zero resistance is placed near a long wire carrying current I*sin(ωt).
- The square loop contains an inductor L.
To find:
The peak value of induced current in the loop.
Explanation:
1. Faraday's Law of Electromagnetic Induction:
According to Faraday's law of electromagnetic induction, an induced emf is produced in a closed loop when the magnetic flux passing through the loop changes. The induced emf is given by:
ε = -dΦ/dt,
where ε is the induced emf and dΦ/dt is the rate of change of magnetic flux.
2. Calculation of Magnetic Flux:
The magnetic flux passing through the square loop can be calculated as the product of magnetic field and the area of the loop. The magnetic field produced by the long wire carrying current I*sin(ωt) at a point P on the loop can be given by Ampere's Law:
B = (μ0*I)/(2πr),
where B is the magnetic field, μ0 is the permeability of free space, I is the current, and r is the distance between the long wire and point P on the loop.
3. Calculation of Induced EMF:
The induced emf in the loop can be calculated as the rate of change of magnetic flux. Since the magnetic field produced by the long wire is constant, the rate of change of magnetic flux is zero. Hence, the induced emf is zero.
4. Calculation of Induced Current:
Since the induced emf is zero, there is no current induced in the loop.
Conclusion:
The peak value of induced current in the loop is zero.
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A conducting square loop pqrs of zero resistance but containing an inductor l is placed near a long wire carrying current isin(omegat) as shown in figure. Find the peak value of induced current in the loop?
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A conducting square loop pqrs of zero resistance but containing an inductor l is placed near a long wire carrying current isin(omegat) as shown in figure. Find the peak value of induced current in the loop? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A conducting square loop pqrs of zero resistance but containing an inductor l is placed near a long wire carrying current isin(omegat) as shown in figure. Find the peak value of induced current in the loop? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A conducting square loop pqrs of zero resistance but containing an inductor l is placed near a long wire carrying current isin(omegat) as shown in figure. Find the peak value of induced current in the loop?.
A conducting square loop pqrs of zero resistance but containing an inductor l is placed near a long wire carrying current isin(omegat) as shown in figure. Find the peak value of induced current in the loop? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A conducting square loop pqrs of zero resistance but containing an inductor l is placed near a long wire carrying current isin(omegat) as shown in figure. Find the peak value of induced current in the loop? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A conducting square loop pqrs of zero resistance but containing an inductor l is placed near a long wire carrying current isin(omegat) as shown in figure. Find the peak value of induced current in the loop?.
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