Question

Find the length of the conductor which is moving with a speed of 5 m/s in a direction perpendicular to the magnetic field of induction 2 tesla if it induces an emf of 10 V between the ends of the conductor.

• A. 1m
• B. 2 m
• C. 3 m
• D. 4 m

Answer 1

The Correct Option is A

To solve the problem, we need to find the length of the conductor moving in a magnetic field, which induces an emf. We are given:
- Speed \( v = 5 \, \text{m/s} \)
- Magnetic field \( B = 2 \, \text{T} \)
- Induced emf \( \varepsilon = 10 \, \text{V} \)

1. Understanding the Formula:
The emf induced in a straight conductor moving perpendicular to a magnetic field is given by:

\( \varepsilon = B \cdot l \cdot v \)
where:
- \( \varepsilon \) is the induced emf
- \( B \) is the magnetic field
- \( l \) is the length of the conductor
- \( v \) is the velocity

2. Substituting the Given Values:
\( 10 = 2 \cdot l \cdot 5 \)

3. Solving for \( l \):

\( 10 = 10l \)

\( l = \frac{10}{10} = 1 \, \text{m} \)

Final Answer:

The length of the conductor is \({1 \, \text{m}} \).