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The magnetic field in a region is given by . A square loop of side d is placed with its edges along the x and y-axis. The loop is moved with a constant velocity . The emf induced in the loop is
a.
b.
c.?
a.
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c.?
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The magnetic field in a region is given by . A square loop of side d i...
Analysis of induced emf in a moving square loop
Induced emf depends on the rate of change of magnetic flux through the loop. Let's analyze the situation step by step.
Magnetic field and velocity of the loop
- The magnetic field in the region is given by the expression provided.
- The square loop of side d is moved with a constant velocity v.
Flux through the loop
- As the loop moves, the magnetic flux through it changes.
- The flux through the loop can be calculated by integrating the magnetic field over the surface of the loop.
Rate of change of flux
- The rate of change of flux through the loop is directly proportional to the velocity of the loop.
- Mathematically, it can be expressed as dΦ/dt = B*d*v, where B is the magnetic field and d is the side length of the square loop.
Induced emf
- The induced emf in the loop is given by Faraday's law of electromagnetic induction, which states that the emf is equal to the rate of change of flux through the loop.
- Therefore, the induced emf in the moving square loop is given by emf = -dΦ/dt = -B*d*v.
So, the correct answer is a. -B*d*v.
Induced emf depends on the rate of change of magnetic flux through the loop. Let's analyze the situation step by step.
Magnetic field and velocity of the loop
- The magnetic field in the region is given by the expression provided.
- The square loop of side d is moved with a constant velocity v.
Flux through the loop
- As the loop moves, the magnetic flux through it changes.
- The flux through the loop can be calculated by integrating the magnetic field over the surface of the loop.
Rate of change of flux
- The rate of change of flux through the loop is directly proportional to the velocity of the loop.
- Mathematically, it can be expressed as dΦ/dt = B*d*v, where B is the magnetic field and d is the side length of the square loop.
Induced emf
- The induced emf in the loop is given by Faraday's law of electromagnetic induction, which states that the emf is equal to the rate of change of flux through the loop.
- Therefore, the induced emf in the moving square loop is given by emf = -dΦ/dt = -B*d*v.
So, the correct answer is a. -B*d*v.
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The magnetic field in a region is given by . A square loop of side d is placed with its edges along the x and y-axis. The loop is moved with a constant velocity . The emf induced in the loop isa. b. c.?
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