Question

A conductor of length 1.75 metre moves at right angles to a uniform magnetic field of flux density 0.5 Wb/m\(^{2}\) with a velocity of 60 metre/second. Calculate the e.m.f. induced in it.

• A. 210 V
• B. 17.5 V
• C. 68.5 V
• D. 52.5 V

Hint:

To simplify calculations with \( 0.5 \), multiply the other whole number by \( 0.5 \) first:
\[ 60 \times 0.5 = 30 \] Then, perform the remaining multiplication:
\[ 30 \times 1.75 = 52.5 \]

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
When a straight conductor moves through a magnetic field, it cuts across the magnetic flux lines, which induces an electromotive force (dynamically induced EMF) across its ends.
Key Formula or Approach:
The magnitude of the dynamically induced EMF (\( e \)) in a moving conductor is given by the formula:
\[ e = B \cdot L \cdot v \cdot \sin\theta \] Where:
- \( B \) is the magnetic flux density in Tesla or \(\text{Wb/m}^2\).
- \( L \) is the active length of the conductor in meters.
- \( v \) is the linear velocity of the conductor in meters per second.
- \(\theta\) is the angle between the direction of motion of the conductor and the magnetic field.

Step 2: Detailed Explanation:
Let us extract and substitute the given values:
- Length of conductor (\( L \)) = \( 1.75 \text{ m} \)
- Magnetic flux density (\( B \)) = \( 0.5 \text{ Wb/m}^2 \)
- Velocity (\( v \)) = \( 60 \text{ m/s} \)
- Angle (\(\theta\)) = \( 90^{\circ} \) (since it moves at right angles, and \(\sin 90^{\circ} = 1\))
Now, calculate the induced EMF:
\[ e = 0.5 \times 1.75 \times 60 \times \sin(90^{\circ}) \] Rearrange the terms to simplify multiplication:
\[ e = (0.5 \times 60) \times 1.75 \times 1 \] \[ e = 30 \times 1.75 \] \[ e = 52.5 \text{ V} \] Therefore, the induced EMF is \( 52.5 \text{ V} \).

Step 3: Final Answer:
The induced e.m.f. in the conductor is 52.5 V.