A conducting rod of 1 m length and 1 kg mass is suspended by two verticle wires through its ends. An external magnetic field of 2T is applied normal to the rod. Now the current to be passed through the rod so as to make the tension in the wire zero is
[Take `g = 10 ms^(-2)]`

Options

A. 15 A
B. `5 A`
C. `1.5 A`
D. `2.5 A`

Answer

To solve the problem, we need to find the current that should be passed through the conducting rod so that the tension in the supporting wires becomes zero. Here's the step-by-step solution:

### Step 1: Understand the Forces Acting on the Rod
The rod has two main forces acting on it:
1. The gravitational force (weight) acting downwards, which is given by \( F_g = mg \).
2. The magnetic force acting upwards when current flows through the rod in a magnetic field.

### Step 2: Calculate the Weight of the Rod
Given:
- Mass of the rod, \( m = 1 \, \text{kg} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

The weight of the rod can be calculated as:
\[ F_g = mg = 1 \, \text{kg} \times 10 \, \text{m/s}^2 = 10 \, \text{N} \]

### Step 3: Set Up the Equation for Zero Tension
For the tension in the wires to be zero, the magnetic force \( F_B \) must equal the weight of the rod:
\[ F_B = F_g \]
Thus,
\[ F_B = 10 \, \text{N} \]

### Step 4: Calculate the Magnetic Force
The magnetic force on a current-carrying conductor in a magnetic field is given by the formula:
\[ F_B = I \cdot L \cdot B \]
Where:
- \( I \) is the current in amperes,
- \( L \) is the length of the rod (1 m),
- \( B \) is the magnetic field strength (2 T).

Substituting the known values into the equation:
\[ F_B = I \cdot 1 \, \text{m} \cdot 2 \, \text{T} \]
\[ F_B = 2I \]

### Step 5: Set the Magnetic Force Equal to the Weight
Now, we set the magnetic force equal to the weight of the rod:
\[ 2I = 10 \, \text{N} \]

### Step 6: Solve for the Current \( I \)
To find \( I \), we rearrange the equation:
\[ I = \frac{10 \, \text{N}}{2} = 5 \, \text{A} \]

### Conclusion
The current that needs to be passed through the rod to make the tension in the wires zero is:
\[ \boxed{5 \, \text{A}} \]