. A rectangular loop of dimensions / and w moves with a constant speed...
Introduction:
A rectangular loop of dimensions l and w is moving with a constant speed v through a region containing a uniform magnetic field B directed into the paper. The magnetic field extends a distance of 4w. We need to determine the variation of the induced electromotive force (emf) with the position (x) of the front end of the loop.
Explanation:
1. Relationship between emf and magnetic field:
According to Faraday's law of electromagnetic induction, the emf induced in a loop is directly proportional to the rate of change of magnetic flux through the loop. The magnetic flux through a loop is given by the product of the magnetic field (B) and the area (A) of the loop.
2. Variation of magnetic flux with position:
As the loop moves through the magnetic field, the magnetic flux through the loop changes. The magnetic flux is maximum when the loop is completely inside the magnetic field and decreases as the loop moves out of the field.
3. Variation of emf with position:
Based on the above relationship, we can conclude the following:
- When the loop is completely inside the magnetic field (x = 0), the magnetic flux is maximum, and therefore the emf induced in the loop is also maximum.
- As the loop moves out of the magnetic field (x > 0), the magnetic flux decreases, resulting in a decrease in the induced emf.
- When the loop is completely outside the magnetic field (x = 4w), the magnetic flux is zero, and therefore the induced emf is also zero.
4. Correct representation of emf variation with position:
Based on the above analysis, we can conclude that the correct representation of the variation of emf (ɛ) with the position (x) of the front end of the loop is as follows:
- Initially, when the loop is inside the magnetic field (x = 0), the emf is maximum.
- As the loop moves out of the magnetic field, the emf decreases.
- When the loop is completely outside the magnetic field (x = 4w), the emf is zero.
Therefore, the correct figure representing the variation of emf (ɛ) with the position (x) of the front end of the loop would be a decreasing graph that starts at a maximum value and reaches zero at x = 4w.