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