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

Explanation

To find the force on the conductor in the form of a right angle `ABC`, we can follow these steps:

### Step 1: Identify the Given Data
- Length of `AB` = 3 cm = 0.03 m (convert to meters)
- Length of `BC` = 4 cm = 0.04 m (convert to meters)
- Current, `I` = 10 A
- Magnetic field, `B` = 5 T

### Step 2: Calculate the Force on Each Segment of the Conductor
The force on a straight conductor carrying current in a magnetic field can be calculated using the formula:
\[ F = B \cdot I \cdot L \]
where:
- \( F \) = force on the conductor
- \( B \) = magnetic field strength
- \( I \) = current
- \( L \) = length of the conductor segment

#### Force on Segment `AB`
- Length of `AB` = 0.03 m
- Using the formula:
\[ F_{AB} = B \cdot I \cdot L_{AB} = 5 \, \text{T} \cdot 10 \, \text{A} \cdot 0.03 \, \text{m} \]
\[ F_{AB} = 5 \cdot 10 \cdot 0.03 = 1.5 \, \text{N} \]

#### Force on Segment `BC`
- Length of `BC` = 0.04 m
- Using the formula:
\[ F_{BC} = B \cdot I \cdot L_{BC} = 5 \, \text{T} \cdot 10 \, \text{A} \cdot 0.04 \, \text{m} \]
\[ F_{BC} = 5 \cdot 10 \cdot 0.04 = 2.0 \, \text{N} \]

### Step 3: Determine the Direction of Forces
- The force on segment `AB` will be directed out of the plane of the paper (using the right-hand rule).
- The force on segment `BC` will be directed into the plane of the paper.

### Step 4: Calculate the Net Force
Since the forces on segments `AB` and `BC` are in opposite directions, we can find the net force by subtracting the smaller force from the larger force:
\[ F_{net} = F_{BC} - F_{AB} = 2.0 \, \text{N} - 1.5 \, \text{N} = 0.5 \, \text{N} \]

### Conclusion
The total force acting on the conductor is \( 0.5 \, \text{N} \).