Question

A straight wire 15.0 m long moves at 1.5 m/s perpendicularly through a 2.0 T magnetic field. What is the induced E M F?

Group of answer choices

15 V

1.5 V

45 V

22.5 V

Answer 1

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

\[
\text{E.M.F.} = B \cdot L \cdot v
\]

where:
- \( B \) is the magnetic field strength (in teslas, T),
- \( L \) is the length of the wire (in meters, m),
- \( v \) is the velocity of the wire (in meters per second, m/s).

Given:
- \( B = 2.0 \, \text{T} \)
- \( L = 15.0 \, \text{m} \)
- \( v = 1.5 \, \text{m/s} \)

Now, substituting the known values into the formula:

\[
\text{E.M.F.} = 2.0 \, \text{T} \cdot 15.0 \, \text{m} \cdot 1.5 \, \text{m/s}
\]

Calculating:

\[
\text{E.M.F.} = 2.0 \cdot 15.0 \cdot 1.5 = 45.0 \, \text{V}
\]

Thus, the induced E.M.F. is **45 V**.

Therefore, the correct answer is **45 V**.