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

1 answer

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.