A straight wire of length `0.5` metre and carrying a current of `1.2` ampere is placed in a uniform magnetic field of induction 2 tesla. If the magnetic field is perpendicular to the length of the wire , the force acting on the wire is

Options

A. 2.4 N
B. 1.2 N
C. 3.0 N
D. 2.0 N

Answer

To solve the problem, we will use the formula for the magnetic force acting on a current-carrying wire in a magnetic field. The formula is given by:

\[ F = BIL \sin \theta \]

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

### Step-by-Step Solution:

1. **Identify the given values**:
- Length of the wire, \( L = 0.5 \, \text{m} \)
- Current, \( I = 1.2 \, \text{A} \)
- Magnetic field induction, \( B = 2 \, \text{T} \)
- Angle \( \theta = 90^\circ \) (since the magnetic field is perpendicular to the wire)

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

3. **Plug in the values**:
\[ F = (2 \, \text{T}) \times (1.2 \, \text{A}) \times (0.5 \, \text{m}) \]

4. **Calculate the force**:
\[ F = 2 \times 1.2 \times 0.5 = 1.2 \, \text{N} \]

5. **Conclusion**:
The force acting on the wire is \( 1.2 \, \text{N} \).

### Final Answer:
The force acting on the wire is \( 1.2 \, \text{N} \).

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