Question

A conductor moving with a speed of 20 m/s in the direction perpendicular to the direction of magnetic field of induction 0.5 T, induces an EMF of 5 V. The length of the conductor is

• A. 1 m
• B. 5 m
• C. 50 m
• D. 0.5 m

Answer 1

The Correct Option is D

Step 1: Recall the formula for induced EMF in a moving conductor.

The EMF (\( \varepsilon \)) induced in a conductor moving in a magnetic field is given by:

\[ \varepsilon = B \cdot v \cdot l, \]

where:

• \( \varepsilon \) is the induced EMF (in volts),
• \( B \) is the magnetic field strength (in tesla),
• \( v \) is the velocity of the conductor (in m/s), and
• \( l \) is the length of the conductor (in meters).

 

Step 2: Substitute the given values into the formula.

We are given:

• \( \varepsilon = 5 \, \text{V}, \)
• \( B = 0.5 \, \text{T}, \)
• \( v = 20 \, \text{m/s}. \)

Substitute these values into the formula:

 

\[ 5 = 0.5 \cdot 20 \cdot l. \]

Step 3: Solve for \( l \).

Simplify the equation:

\[ 5 = 10 \cdot l. \]

Rearrange to isolate \( l \):

\[ l = \frac{5}{10} = 0.5 \, \text{m}. \]

Final Answer: The length of the conductor is \( \mathbf{0.5 \, \text{m}} \), which corresponds to option \( \mathbf{(4)} \).