In the previous example find the mass of the wire if the magnetic field is equal to the earth magnetic field `(4 xx 10^(-5) T)`, current in the wire is 5 A and length of the wire is 1m. The wire remains suspended in mid air in equilibrium. (take `g = 10 m//s^(2)`)

Answer

To find the mass of the wire suspended in the magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Forces Acting on the Wire:**
The wire is in equilibrium, meaning the gravitational force acting downward is balanced by the magnetic force acting upward. Therefore, we can write the equation:
\[ F_g = F_m \]
where \( F_g \) is the gravitational force and \( F_m \) is the magnetic force.

2. **Express the Gravitational Force:**
The gravitational force acting on the wire can be expressed as:
\[ F_g = mg \]
where \( m \) is the mass of the wire and \( g \) is the acceleration due to gravity. Given \( g = 10 \, \text{m/s}^2 \), we have:
\[ F_g = m \cdot 10 \]

3. **Express the Magnetic Force:**
The magnetic force on the wire can be expressed using the formula:
\[ F_m = BIL \]
where \( B \) is the magnetic field strength, \( I \) is the current flowing through the wire, and \( L \) is the length of the wire. Given \( B = 4 \times 10^{-5} \, \text{T} \), \( I = 5 \, \text{A} \), and \( L = 1 \, \text{m} \), we have:
\[ F_m = (4 \times 10^{-5}) \cdot (5) \cdot (1) \]

4. **Calculate the Magnetic Force:**
Now, substituting the values into the equation for magnetic force:
\[ F_m = 4 \times 10^{-5} \cdot 5 \cdot 1 = 20 \times 10^{-5} \, \text{N} = 2 \times 10^{-4} \, \text{N} \]

5. **Set the Forces Equal:**
Since \( F_g = F_m \), we can set the two equations equal to each other:
\[ mg = 2 \times 10^{-4} \]

6. **Solve for Mass \( m \):**
Now, substituting \( g = 10 \):
\[ m \cdot 10 = 2 \times 10^{-4} \]
\[ m = \frac{2 \times 10^{-4}}{10} = 2 \times 10^{-5} \, \text{kg} \]

7. **Convert Mass to Grams:**
To convert the mass from kilograms to grams, we multiply by 1000:
\[ m = 2 \times 10^{-5} \, \text{kg} \times 1000 = 2 \times 10^{-2} \, \text{g} = 0.02 \, \text{g} \]

### Final Answer:
The mass of the wire is \( 0.02 \, \text{g} \).

---