A conductor in the form of a right angle `ABC` with `AB=3 cm` and `BC = 4 cm` carries a current of `10 A`.There is a uniform magnetic field of `5 T` perpendicular to the palne of the conductor. The force on the conductor will be

Options

A. 1.5 N
B. 2.0 N
C. 2.5 N
D. 3.5 N

Answer

To solve the problem, we need to calculate the force acting on the conductor in the shape of a right angle triangle ABC, where AB = 3 cm, BC = 4 cm, and the current flowing through it is 10 A. The magnetic field is given as 5 T, and it is perpendicular to the plane of the conductor.

### Step-by-Step Solution:

1. **Identify the Length of the Conductor:**
- The conductor consists of two segments: AB and BC.
- We need to find the length of the hypotenuse AC using the Pythagorean theorem.
- The lengths are:
- AB = 3 cm
- BC = 4 cm
- Using the Pythagorean theorem:
\[ AC = \sqrt{AB^2 + BC^2} = \sqrt{(3 \, \text{cm})^2 + (4 \, \text{cm})^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, \text{cm} \]

2. **Convert Length to Meters:**
- Since the SI unit for length is meters, we convert 5 cm to meters:
\[ L = 5 \, \text{cm} = 5 \times 10^{-2} \, \text{m} \]

3. **Use the Formula for Magnetic Force:**
- The formula for the magnetic force (F) on a current-carrying conductor in a magnetic field is given by:
\[ F = I \cdot L \cdot B \]
- Where:
- \( I = 10 \, \text{A} \) (current)
- \( L = 5 \times 10^{-2} \, \text{m} \) (length of the conductor)
- \( B = 5 \, \text{T} \) (magnetic field strength)

4. **Substitute the Values into the Formula:**
- Now substituting the values into the formula:
\[ F = 10 \, \text{A} \cdot (5 \times 10^{-2} \, \text{m}) \cdot 5 \, \text{T} \]
- Calculating:
\[ F = 10 \cdot 5 \cdot 5 \times 10^{-2} = 250 \times 10^{-2} = 2.5 \, \text{N} \]

5. **Conclusion:**
- The force on the conductor is:
\[ F = 2.5 \, \text{N} \]

### Final Answer:
The force on the conductor will be **2.5 N**.