A current of 1 A flows a wire of length 0.1 m in a magnetic field of 0.5 T. The force acting on the wire when it makes an angle of `90^(@)` with the field is

Options

A. zero
B. 0.05 N
C. 1 N
D. 0.5 N

Answer

To find the force acting on a wire carrying a current in a magnetic field, we can use the formula:

\[ F = I \cdot L \cdot B \cdot \sin(\theta) \]

Where:
- \( F \) is the force,
- \( I \) is the current in amperes,
- \( L \) is the length of the wire in meters,
- \( B \) is the magnetic field in teslas,
- \( \theta \) is the angle between the wire and the magnetic field.

### Step-by-Step Solution:

1. **Identify the given values:**
- Current, \( I = 1 \, \text{A} \)
- Length of the wire, \( L = 0.1 \, \text{m} \)
- Magnetic field, \( B = 0.5 \, \text{T} \)
- Angle, \( \theta = 90^\circ \)

2. **Substitute the angle into the formula:**
Since \( \theta = 90^\circ \), we know that \( \sin(90^\circ) = 1 \). Therefore, the formula simplifies to:
\[ F = I \cdot L \cdot B \cdot \sin(90^\circ) = I \cdot L \cdot B \]

3. **Plug in the values:**
Now substitute the known values into the equation:
\[ F = 1 \, \text{A} \cdot 0.1 \, \text{m} \cdot 0.5 \, \text{T} \]

4. **Calculate the force:**
\[ F = 1 \cdot 0.1 \cdot 0.5 = 0.05 \, \text{N} \]

5. **Conclusion:**
The force acting on the wire when it makes an angle of \( 90^\circ \) with the magnetic field is \( 0.05 \, \text{N} \).

### Final Answer:
The force acting on the wire is \( 0.05 \, \text{N} \).