7. A rod of length \( 0.5 \, \text{m} \) moves with a velocity of \( 2 \, \text{m/s} \) perpendicular to a uniform magnetic field of strength \( 0.4 \, \text{T} \). What is the induced emf in the rod?
The induced EMF (\( \mathcal{E} \)) in a rod moving perpendicular to a magnetic field is given by the formula:
\[ \mathcal{E} = B \cdot v \cdot l \]
Where:
- \( B = 0.4 \, \text{T} \): Magnetic field strength
- \( v = 2 \, \text{m/s} \): Velocity of the rod
- \( l = 0.5 \, \text{m} \): Length of the rod
Substitute the given values:
\[ \mathcal{E} = 0.4 \cdot 2 \cdot 0.5 \]
First, calculate \( 2 \cdot 0.5 \):
\[ 2 \cdot 0.5 = 1 \]
Now calculate \( \mathcal{E} \):
\[ \mathcal{E} = 0.4 \cdot 1 = 0.4 \, \text{V} \]
Thus, the induced EMF in the rod is:
\[ \mathcal{E} = 0.4 \, \text{V} \]
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