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A conducting circular loop of radius 20 cm lies in the z = 0 plane in a field B = 20 cos 377t az mWb/m2. The induced voltage in the loop is
- a)- 0.95 sin 377t V
- b)0.95 sin 377t V
- c)- 0.95 cos 377t V
- d)0.95 cos 377t V
Correct answer is option 'B'. Can you explain this answer?
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A conducting circular loop of radius 20 cm lies in the z = 0 plane in...
Given:
To Find:
The induced voltage in the loop.
Solution:
The induced voltage in a conductor is given by Faraday's law of electromagnetic induction, which states that the voltage induced in a loop is equal to the time derivative of the magnetic flux passing through the loop. Mathematically, it can be written as:
e = -dΦ/dt
where e is the induced voltage, Φ is the magnetic flux, and t is time.
Step 1: Calculate the magnetic flux passing through the loop.
The magnetic flux passing through the loop can be calculated using the formula:
Φ = ∫B.dA
where B is the magnetic field and dA is the differential area of the loop.
For a circular loop, the differential area can be written as dA = rdrdθ (where r is the radius of the loop and θ is the angle between the normal to the loop and the z-axis).
Hence, the flux passing through the loop is:
Φ = ∫B.dA = ∫(Bcosθ)dA = B∫cosθdA = B∫rdrdθ = Bπr^2
Substituting the given values, we get:
Φ = (20 cos 377t)(π(0.2)^2) = 0.02513 cos 377t Wb
Step 2: Calculate the induced voltage.
The induced voltage can be calculated using the formula:
e = -dΦ/dt
Taking the time derivative of Φ, we get:
dΦ/dt = -0.02513(377) sin 377t
Substituting this value in the above formula, we get:
e = -(-0.02513(377) sin 377t) = 0.95 sin 377t V
Hence, the induced voltage in the loop is 0.95 sin 377t V.
Answer:
The correct option is (B) 0.95 sin 377t V.
- Radius of the circular loop, r = 20 cm
- Magnetic field, B = 20 cos 377t az mWb/m^2
To Find:
The induced voltage in the loop.
Solution:
The induced voltage in a conductor is given by Faraday's law of electromagnetic induction, which states that the voltage induced in a loop is equal to the time derivative of the magnetic flux passing through the loop. Mathematically, it can be written as:
e = -dΦ/dt
where e is the induced voltage, Φ is the magnetic flux, and t is time.
Step 1: Calculate the magnetic flux passing through the loop.
The magnetic flux passing through the loop can be calculated using the formula:
Φ = ∫B.dA
where B is the magnetic field and dA is the differential area of the loop.
For a circular loop, the differential area can be written as dA = rdrdθ (where r is the radius of the loop and θ is the angle between the normal to the loop and the z-axis).
Hence, the flux passing through the loop is:
Φ = ∫B.dA = ∫(Bcosθ)dA = B∫cosθdA = B∫rdrdθ = Bπr^2
Substituting the given values, we get:
Φ = (20 cos 377t)(π(0.2)^2) = 0.02513 cos 377t Wb
Step 2: Calculate the induced voltage.
The induced voltage can be calculated using the formula:
e = -dΦ/dt
Taking the time derivative of Φ, we get:
dΦ/dt = -0.02513(377) sin 377t
Substituting this value in the above formula, we get:
e = -(-0.02513(377) sin 377t) = 0.95 sin 377t V
Hence, the induced voltage in the loop is 0.95 sin 377t V.
Answer:
The correct option is (B) 0.95 sin 377t V.
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A conducting circular loop of radius 20 cm lies in the z = 0 plane in a field B = 20 cos 377t az mWb/m2. The induced voltage in the loop isa)- 0.95 sin 377t Vb)0.95 sin 377t Vc)- 0.95 cos 377t Vd)0.95 cos 377t VCorrect answer is option 'B'. Can you explain this answer?
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