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A plane loop shown in figure is shaped as two squares with sides a and band is introduced into a uniform magnetic field at right angles to the loop's plane. The magnetic induction varies with time as B = B sin wt, Find the amplitude of the current induced in the loop if its resistance per unit length is equal to p. (The inductance of the loop is to be neglected)?
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A plane loop shown in figure is shaped as two squares with sides a and...
Introduction:
In this problem, we are given a plane loop shaped as two squares with sides a and b. The loop is introduced into a uniform magnetic field at right angles to the loop's plane. The magnetic induction varies with time as B = B sin wt. We need to find the amplitude of the current induced in the loop if its resistance per unit length is equal to p. We will neglect the inductance of the loop.
Given:
- Plane loop shaped as two squares with sides a and b
- Magnetic induction varies with time as B = B sin wt
- Resistance per unit length of the loop is p
Approach:
To find the amplitude of the current induced in the loop, we can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced emf in a closed loop is equal to the rate of change of magnetic flux through the loop.
Step 1: Calculate the magnetic flux through the loop:
The magnetic flux through the loop can be calculated using the formula:
Φ = B * A * cosθ
where B is the magnetic induction, A is the area of the loop, and θ is the angle between the magnetic field and the normal to the loop.
In this case, the magnetic field is at right angles to the loop's plane, so θ = 90°. Therefore, cosθ = 0.
Thus, the magnetic flux through the loop is:
Φ = B * A * 0 = 0
Step 2: Calculate the induced emf:
The induced emf can be calculated using the formula:
ε = -dΦ/dt
where ε is the induced emf and dΦ/dt is the rate of change of magnetic flux through the loop.
Since the magnetic flux through the loop is constant (0), the rate of change of magnetic flux is also 0.
Therefore, the induced emf is:
ε = -dΦ/dt = -0 = 0
Step 3: Calculate the current induced:
The current induced in the loop can be calculated using Ohm's law:
I = ε/R
where I is the current induced, ε is the induced emf, and R is the resistance per unit length of the loop.
Since the induced emf is 0, the current induced in the loop is also 0.
Conclusion:
The amplitude of the current induced in the loop is 0.
In this problem, we are given a plane loop shaped as two squares with sides a and b. The loop is introduced into a uniform magnetic field at right angles to the loop's plane. The magnetic induction varies with time as B = B sin wt. We need to find the amplitude of the current induced in the loop if its resistance per unit length is equal to p. We will neglect the inductance of the loop.
Given:
- Plane loop shaped as two squares with sides a and b
- Magnetic induction varies with time as B = B sin wt
- Resistance per unit length of the loop is p
Approach:
To find the amplitude of the current induced in the loop, we can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced emf in a closed loop is equal to the rate of change of magnetic flux through the loop.
Step 1: Calculate the magnetic flux through the loop:
The magnetic flux through the loop can be calculated using the formula:
Φ = B * A * cosθ
where B is the magnetic induction, A is the area of the loop, and θ is the angle between the magnetic field and the normal to the loop.
In this case, the magnetic field is at right angles to the loop's plane, so θ = 90°. Therefore, cosθ = 0.
Thus, the magnetic flux through the loop is:
Φ = B * A * 0 = 0
Step 2: Calculate the induced emf:
The induced emf can be calculated using the formula:
ε = -dΦ/dt
where ε is the induced emf and dΦ/dt is the rate of change of magnetic flux through the loop.
Since the magnetic flux through the loop is constant (0), the rate of change of magnetic flux is also 0.
Therefore, the induced emf is:
ε = -dΦ/dt = -0 = 0
Step 3: Calculate the current induced:
The current induced in the loop can be calculated using Ohm's law:
I = ε/R
where I is the current induced, ε is the induced emf, and R is the resistance per unit length of the loop.
Since the induced emf is 0, the current induced in the loop is also 0.
Conclusion:
The amplitude of the current induced in the loop is 0.
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A plane loop shown in figure is shaped as two squares with sides a and band is introduced into a uniform magnetic field at right angles to the loop's plane. The magnetic induction varies with time as B = B sin wt, Find the amplitude of the current induced in the loop if its resistance per unit length is equal to p. (The inductance of the loop is to be neglected)? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A plane loop shown in figure is shaped as two squares with sides a and band is introduced into a uniform magnetic field at right angles to the loop's plane. The magnetic induction varies with time as B = B sin wt, Find the amplitude of the current induced in the loop if its resistance per unit length is equal to p. (The inductance of the loop is to be neglected)? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plane loop shown in figure is shaped as two squares with sides a and band is introduced into a uniform magnetic field at right angles to the loop's plane. The magnetic induction varies with time as B = B sin wt, Find the amplitude of the current induced in the loop if its resistance per unit length is equal to p. (The inductance of the loop is to be neglected)?.
A plane loop shown in figure is shaped as two squares with sides a and band is introduced into a uniform magnetic field at right angles to the loop's plane. The magnetic induction varies with time as B = B sin wt, Find the amplitude of the current induced in the loop if its resistance per unit length is equal to p. (The inductance of the loop is to be neglected)? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A plane loop shown in figure is shaped as two squares with sides a and band is introduced into a uniform magnetic field at right angles to the loop's plane. The magnetic induction varies with time as B = B sin wt, Find the amplitude of the current induced in the loop if its resistance per unit length is equal to p. (The inductance of the loop is to be neglected)? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plane loop shown in figure is shaped as two squares with sides a and band is introduced into a uniform magnetic field at right angles to the loop's plane. The magnetic induction varies with time as B = B sin wt, Find the amplitude of the current induced in the loop if its resistance per unit length is equal to p. (The inductance of the loop is to be neglected)?.
Solutions for A plane loop shown in figure is shaped as two squares with sides a and band is introduced into a uniform magnetic field at right angles to the loop's plane. The magnetic induction varies with time as B = B sin wt, Find the amplitude of the current induced in the loop if its resistance per unit length is equal to p. (The inductance of the loop is to be neglected)? in English & in Hindi are available as part of our courses for JEE.
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A plane loop shown in figure is shaped as two squares with sides a and band is introduced into a uniform magnetic field at right angles to the loop's plane. The magnetic induction varies with time as B = B sin wt, Find the amplitude of the current induced in the loop if its resistance per unit length is equal to p. (The inductance of the loop is to be neglected)?, a detailed solution for A plane loop shown in figure is shaped as two squares with sides a and band is introduced into a uniform magnetic field at right angles to the loop's plane. The magnetic induction varies with time as B = B sin wt, Find the amplitude of the current induced in the loop if its resistance per unit length is equal to p. (The inductance of the loop is to be neglected)? has been provided alongside types of A plane loop shown in figure is shaped as two squares with sides a and band is introduced into a uniform magnetic field at right angles to the loop's plane. The magnetic induction varies with time as B = B sin wt, Find the amplitude of the current induced in the loop if its resistance per unit length is equal to p. (The inductance of the loop is to be neglected)? theory, EduRev gives you an
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