A wire of mass 100 g, length 1 m and current 5 A is balanced in mid air by a magnetic field B, then find the value of B.

Options

A. a. 0.2 T
B. b. 0.1 T
C. c. 0.5 T
D. d. 0.6 T

Explanation

To solve the problem, we need to find the value of the magnetic field \( B \) that balances the weight of a wire carrying a current. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Mass of the wire, \( m = 100 \, \text{g} = 0.1 \, \text{kg} \) (since \( 1 \, \text{g} = 10^{-3} \, \text{kg} \))
- Length of the wire, \( l = 1 \, \text{m} \)
- Current through the wire, \( I = 5 \, \text{A} \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)

### Step 2: Calculate the weight of the wire
The weight \( W \) of the wire can be calculated using the formula:
\[ W = m \cdot g \]
Substituting the values:
\[ W = 0.1 \, \text{kg} \cdot 9.8 \, \text{m/s}^2 = 0.98 \, \text{N} \]

### Step 3: Use the formula for the magnetic force
The magnetic force \( F_B \) acting on the wire can be calculated using the formula:
\[ F_B = I \cdot l \cdot B \]
Where:
- \( I \) is the current in the wire,
- \( l \) is the length of the wire,
- \( B \) is the magnetic field strength.

### Step 4: Set the magnetic force equal to the weight
Since the wire is balanced in mid-air, the magnetic force must equal the weight of the wire:
\[ F_B = W \]
Thus,
\[ I \cdot l \cdot B = m \cdot g \]

### Step 5: Solve for the magnetic field \( B \)
Rearranging the equation to solve for \( B \):
\[ B = \frac{m \cdot g}{I \cdot l} \]
Substituting the known values:
\[ B = \frac{0.1 \, \text{kg} \cdot 9.8 \, \text{m/s}^2}{5 \, \text{A} \cdot 1 \, \text{m}} = \frac{0.98 \, \text{N}}{5 \, \text{A}} = 0.196 \, \text{T} \]

### Step 6: Round the answer
Rounding \( 0.196 \, \text{T} \) to two decimal places gives:
\[ B \approx 0.2 \, \text{T} \]

### Final Answer
The value of the magnetic field \( B \) is approximately **0.2 T**.

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