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A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the direction of magnetic field. The radius of the loop is made to shrink at a constant rate of 1 mm s-1. Find the induced emf in the loop when it's radius is 2 cm.
- a)2 πμV
- b)πμV
- c)1 μV
- d)2 μV
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A conducting circular loop is placed in a uniform magnetic field, B = ...
Here;
Magnetic field. B = 0.025 T
Radius of the loop, r = 2 cm = 2 x 10-2 m
Constant rate at which radius of the loop shrinks,
Magnetic flux linked with the loop is
From Faraday's law, the magnitude of the induced emf is
Magnetic field. B = 0.025 T
Radius of the loop, r = 2 cm = 2 x 10-2 m
Constant rate at which radius of the loop shrinks,
Magnetic flux linked with the loop is
From Faraday's law, the magnitude of the induced emf is
Most Upvoted Answer
A conducting circular loop is placed in a uniform magnetic field, B = ...
To find the induced emf in the loop, we can use Faraday's law of electromagnetic induction, which states that the induced emf is equal to the rate of change of magnetic flux through the loop.
The magnetic flux through the loop is given by the equation:
Φ = B*A
Where Φ is the magnetic flux, B is the magnetic field, and A is the area of the loop.
Since the loop is circular, the area can be calculated using the formula:
A = π*r^2
Where A is the area and r is the radius of the loop.
Given that B = 0.025 T and the radius is shrinking at a constant rate of 1 mm/s, we can calculate the magnetic flux when the radius is 2 cm (0.02 m):
Φ = B*A = (0.025 T)*(π*(0.02 m)^2) = 0.025*π*0.0004 = 0.0000314 Wb
Now, to find the induced emf, we need to find the rate of change of the magnetic flux with respect to time. Since the radius is shrinking at a constant rate of 1 mm/s, the rate of change of the magnetic flux is given by:
dΦ/dt = -B*A*(dr/dt)
Where dΦ/dt is the rate of change of magnetic flux, dr/dt is the rate of change of the radius, and the negative sign indicates that the flux is decreasing as the radius shrinks.
The rate of change of the radius is given as 1 mm/s, which is equal to 0.001 m/s.
Substituting the values into the equation, we have:
dΦ/dt = -B*A*(dr/dt) = -0.025*π*0.0004*(0.001 m/s) = -0.0000000314 V/s
Therefore, the induced emf in the loop when its radius is 2 cm is 2 x 10^-8 V/s, or 20 nV/s.
The magnetic flux through the loop is given by the equation:
Φ = B*A
Where Φ is the magnetic flux, B is the magnetic field, and A is the area of the loop.
Since the loop is circular, the area can be calculated using the formula:
A = π*r^2
Where A is the area and r is the radius of the loop.
Given that B = 0.025 T and the radius is shrinking at a constant rate of 1 mm/s, we can calculate the magnetic flux when the radius is 2 cm (0.02 m):
Φ = B*A = (0.025 T)*(π*(0.02 m)^2) = 0.025*π*0.0004 = 0.0000314 Wb
Now, to find the induced emf, we need to find the rate of change of the magnetic flux with respect to time. Since the radius is shrinking at a constant rate of 1 mm/s, the rate of change of the magnetic flux is given by:
dΦ/dt = -B*A*(dr/dt)
Where dΦ/dt is the rate of change of magnetic flux, dr/dt is the rate of change of the radius, and the negative sign indicates that the flux is decreasing as the radius shrinks.
The rate of change of the radius is given as 1 mm/s, which is equal to 0.001 m/s.
Substituting the values into the equation, we have:
dΦ/dt = -B*A*(dr/dt) = -0.025*π*0.0004*(0.001 m/s) = -0.0000000314 V/s
Therefore, the induced emf in the loop when its radius is 2 cm is 2 x 10^-8 V/s, or 20 nV/s.
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A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the direction of magnetic field. The radius of the loop is made to shrink at a constant rate of 1 mm s-1. Find the induced emf in the loop when it's radius is 2 cm.a)2 πμVb)πμVc)1 μVd)2 μVCorrect answer is option 'B'. Can you explain this answer?
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