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A conductor of length 100 cm moves at right angle to a uniform field flux density of 1.5 W6/m2 with a velocity of 50 m/s. The emf induced in the conductor will be
- a)150V
- b)75V
- c)50V
- d)37.5V
Correct answer is option 'B'. Can you explain this answer?
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A conductor of length 100 cm moves at right angle to a uniform field f...
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A conductor of length 100 cm moves at right angle to a uniform field f...
To calculate the emf induced in the conductor, we can use Faraday's Law of electromagnetic induction, which states that the emf induced in a conductor is equal to the rate of change of magnetic flux through the conductor.
Given:
Length of the conductor (l) = 100 cm = 1 m
Field flux density (B) = 1.5 Wb/m²
Velocity of the conductor (v) = 50 m/s
1. Calculate the magnetic flux through the conductor:
The magnetic flux (Φ) through the conductor can be calculated using the formula:
Φ = B * A
where B is the magnetic field flux density and A is the area perpendicular to the field.
Since the conductor is moving at a right angle to the field, the area A is equal to the product of the length of the conductor and its width (l * w).
In this case, the width is not given, so we can assume it to be 1 meter for simplicity.
Therefore, A = l * w = 1 m * 1 m = 1 m²
Substituting the values,
Φ = 1.5 Wb/m² * 1 m² = 1.5 Wb
2. Calculate the rate of change of magnetic flux:
The rate of change of magnetic flux (dΦ/dt) is equal to the derivative of the magnetic flux with respect to time.
Since the conductor is moving at a constant velocity, the rate of change of magnetic flux is zero.
3. Calculate the induced emf:
Using Faraday's Law, the induced emf (ε) is given by:
ε = -dΦ/dt
Since the rate of change of magnetic flux is zero, the induced emf is also zero.
Therefore, the correct answer is option 'B' (75V), which implies that there is no induced emf in the conductor.
Given:
Length of the conductor (l) = 100 cm = 1 m
Field flux density (B) = 1.5 Wb/m²
Velocity of the conductor (v) = 50 m/s
1. Calculate the magnetic flux through the conductor:
The magnetic flux (Φ) through the conductor can be calculated using the formula:
Φ = B * A
where B is the magnetic field flux density and A is the area perpendicular to the field.
Since the conductor is moving at a right angle to the field, the area A is equal to the product of the length of the conductor and its width (l * w).
In this case, the width is not given, so we can assume it to be 1 meter for simplicity.
Therefore, A = l * w = 1 m * 1 m = 1 m²
Substituting the values,
Φ = 1.5 Wb/m² * 1 m² = 1.5 Wb
2. Calculate the rate of change of magnetic flux:
The rate of change of magnetic flux (dΦ/dt) is equal to the derivative of the magnetic flux with respect to time.
Since the conductor is moving at a constant velocity, the rate of change of magnetic flux is zero.
3. Calculate the induced emf:
Using Faraday's Law, the induced emf (ε) is given by:
ε = -dΦ/dt
Since the rate of change of magnetic flux is zero, the induced emf is also zero.
Therefore, the correct answer is option 'B' (75V), which implies that there is no induced emf in the conductor.
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A conductor of length 100 cm moves at right angle to a uniform field flux density of 1.5 W6/m2 with a velocity of 50 m/s. The emf induced in the conductor will bea)150Vb)75Vc)50Vd)37.5VCorrect answer is option 'B'. Can you explain this answer?
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