In the figure shown, the conductor PQ of length is moved from to and then up to with a constant velocity . A uniform magnetic field is perpendicular to the plane of the paper and extends from to and it is zero from . The magnitude of emf induced in the conductor is
1
2
Zero
3
4
Official Solution
Correct Option: (3)
Step 1: Understanding the Question:
The question asks for the magnitude of the induced emf in a rod moving with constant velocity through a region with a spatially limited magnetic field. Step 2: Key Formula or Approach:
The magnitude of motional emf ( ) induced in a conductor of length moving with velocity perpendicular to a uniform magnetic field is:
Step 3: Detailed Explanation:
1. Region : In this region, the conductor is moving through a uniform magnetic field . Since the velocity , field , and length are mutually perpendicular, the induced motional emf is constant and is given by .
2. Region : According to the problem, the magnetic field is zero in this region. Since , there is no magnetic flux change linked with the moving rod, and thus the induced emf is zero.
Looking at the options, option (3) correctly identifies the magnitude and the correct spatial interval where the field is present. Step 4: Final Answer:
The magnitude of emf is for the interval .
