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.