A square loop,circular loop prepared from a straight wire of length L are moved out of a
uniform magnetic field,acting normal to the plane of the paper at a constant velocity
v.Draw the variation of induced emf with time for both the loops. How will the graphs
look
To understand the variation of induced emf with time for both the loops, we need to consider the principles of electromagnetic induction and Faraday's law.
1. Square Loop:
Let's start with the square loop. As the loop is moved out of a uniform magnetic field, the flux through the loop changes over time. According to Faraday's law, the induced emf (ε) in a closed loop is directly proportional to the rate of change of magnetic flux (Φ) through the loop. Mathematically, it can be represented as ε = -dΦ/dt, where negative sign indicates that the induced emf opposes the change in magnetic flux.
When the square loop is moved out of the magnetic field at a constant velocity, the magnetic flux decreases. Initially, as the loop is inside the field, the flux is at maximum. As the loop is gradually moved out, the flux decreases linearly. Therefore, the rate of change of flux (-dΦ/dt) is a constant negative value (assuming the velocity is constant).
Hence, the graph for the induced emf with time for the square loop will be a negative constant line. The emf remains constant and opposes the change in flux.
2. Circular Loop:
Now, let's consider the circular loop made from a straight wire. Similar to the square loop, as the circular loop is moved out of the uniform magnetic field, the flux through the loop changes over time. According to Faraday's law, the induced emf (ε) in a closed loop is directly proportional to the rate of change of magnetic flux (Φ) through the loop.
When the circular loop is moved out of the magnetic field at a constant velocity, the magnetic flux decreases. Initially, as the loop is inside the field, the flux is at maximum. As the loop is gradually moved out, the flux decreases exponentially due to the changing area of the loop.
As the flux decreases, the rate of change of flux (-dΦ/dt) also decreases over time. Hence, the induced emf decreases exponentially with time. The graph for the induced emf with time for the circular loop will be a decreasing exponential curve.
In summary:
Square Loop: The graph for induced emf vs. time will be a negative constant line.
Circular Loop: The graph for induced emf vs. time will be a decreasing exponential curve.