Question

A straight wire 10.0 m long moves at 22.0 m/s perpendicularly through a 1.5 T magnetic field. What is the induced EMF?

Group of answer choices

10 V

330 V

1.5 V

22 V

Answer 1

To find the induced electromotive force (EMF) in a wire moving through a magnetic field, we can use the formula:

\[
\text{EMF} = B \cdot L \cdot v
\]

Where:
- \( B \) is the magnetic field strength (in tesla),
- \( L \) is the length of the wire (in meters),
- \( v \) is the velocity of the wire (in meters per second).

Given:
- \( B = 1.5 \, \text{T} \)
- \( L = 10.0 \, \text{m} \)
- \( v = 22.0 \, \text{m/s} \)

Now, let's substitute the values into the formula:

\[
\text{EMF} = 1.5 \, \text{T} \cdot 10.0 \, \text{m} \cdot 22.0 \, \text{m/s}
\]

Calculating it step by step:

1. Calculate \( 1.5 \, \text{T} \cdot 10.0 \, \text{m} \):
\[
1.5 \cdot 10.0 = 15.0
\]

2. Now calculate \( 15.0 \cdot 22.0 \, \text{m/s} \):
\[
15.0 \cdot 22.0 = 330.0 \, \text{V}
\]

Therefore, the induced EMF is \( 330 \, \text{V} \).

The answer is **330 V**.