Calculate the induced emf if a wire of length 2m moves with the speed of 8m/s perpendicular to a magnetic field of induction 3.5 `Wbm^(-2)`

Options

A. 22 V
B. 44 V
C. 7 V
D. 56 V

Explanation

To calculate the induced electromotive force (emf) in a wire moving through a magnetic field, we can use the formula:

\[ \text{Induced emf} (E) = B \cdot L \cdot v \]

where:
- \(E\) is the induced emf,
- \(B\) is the magnetic field induction (in Weber per square meter, \(Wb/m^2\)),
- \(L\) is the length of the wire (in meters),
- \(v\) is the speed of the wire (in meters per second).

**Step 1: Identify the given values.**
- Length of the wire, \(L = 2 \, m\)
- Speed of the wire, \(v = 8 \, m/s\)
- Magnetic field induction, \(B = 3.5 \, Wb/m^2\)

**Step 2: Substitute the values into the formula.**
\[ E = B \cdot L \cdot v \]
Substituting the values:
\[ E = 3.5 \, Wb/m^2 \cdot 2 \, m \cdot 8 \, m/s \]

**Step 3: Calculate the induced emf.**
\[ E = 3.5 \cdot 2 \cdot 8 \]
Calculating step-by-step:
1. First, calculate \(3.5 \cdot 2 = 7\).
2. Then, calculate \(7 \cdot 8 = 56\).

Thus, the induced emf \(E = 56 \, V\).

**Final Answer:**
The induced emf is \(56 \, V\).

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