A `0.1 m` long conductor carrying a current of `50 A` is perpendicular to a magentic field of `1.25 mT`. The mechanical power to move the conductor with a speed of `1ms^(-1)` is

Options

A. `62.5 mW`
B. `625 mW`
C. `6.25 mW`
D. `12.5 mW`

Explanation

To solve the problem, we need to calculate the mechanical power required to move a conductor in a magnetic field. Here's the step-by-step solution:

### Step 1: Identify the given values
- Length of the conductor (L) = 0.1 m
- Current (I) = 50 A
- Magnetic field strength (B) = 1.25 mT = 1.25 × 10^(-3) T (since 1 mT = 10^(-3) T)
- Speed of the conductor (v) = 1 m/s

### Step 2: Calculate the magnetic force (F) on the conductor
The magnetic force experienced by a current-carrying conductor in a magnetic field is given by the formula:
\[ F = I \cdot L \cdot B \]
Since the conductor is perpendicular to the magnetic field, we can use the formula directly without the sine term.

Substituting the values:
\[ F = 50 \, \text{A} \cdot 0.1 \, \text{m} \cdot (1.25 \times 10^{-3} \, \text{T}) \]
\[ F = 50 \cdot 0.1 \cdot 1.25 \times 10^{-3} \]
\[ F = 6.25 \times 10^{-3} \, \text{N} \]

### Step 3: Calculate the mechanical power (P)
The mechanical power required to move the conductor at a constant speed in the magnetic field can be calculated using the formula:
\[ P = F \cdot v \]
Since the force is in the direction of the velocity, we can use the formula directly.

Substituting the values:
\[ P = (6.25 \times 10^{-3} \, \text{N}) \cdot (1 \, \text{m/s}) \]
\[ P = 6.25 \times 10^{-3} \, \text{W} \]

### Step 4: Convert power to milliwatts
To express the power in milliwatts:
\[ P = 6.25 \times 10^{-3} \, \text{W} = 6.25 \, \text{mW} \]

### Final Answer
The mechanical power required to move the conductor is **6.25 mW**.

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