Two wires A and B of length 5 cm and infinite are kept 5 cm apart. Calculate the force experienced by wire B on A if wire A and B carry current of 10 A and 12 A respectively.

Answer

To solve the problem, we need to calculate the force experienced by wire A due to the magnetic field created by wire B. We will follow these steps:

### Step 1: Understand the Setup
- Wire A has a length of 5 cm and carries a current of \( I_A = 10 \, \text{A} \).
- Wire B is infinitely long and carries a current of \( I_B = 12 \, \text{A} \).
- The distance between the two wires is \( D = 5 \, \text{cm} = 0.05 \, \text{m} \).

### Step 2: Calculate the Magnetic Field due to Wire B at the Location of Wire A
The magnetic field \( B \) at a distance \( D \) from a long straight wire carrying current \( I_B \) is given by the formula:
\[ B = \frac{\mu_0 I_B}{2 \pi D} \]
where \( \mu_0 \) (the permeability of free space) is approximately \( 4\pi \times 10^{-7} \, \text{T m/A} \).

Substituting the values:
\[ B = \frac{4\pi \times 10^{-7} \times 12}{2 \pi \times 0.05} \]
\[ B = \frac{4 \times 10^{-7} \times 12}{0.1} \]
\[ B = \frac{48 \times 10^{-7}}{0.1} = 4.8 \times 10^{-6} \, \text{T} \]

### Step 3: Calculate the Force on Wire A
The force \( F \) experienced by a length \( L \) of wire A in a magnetic field \( B \) is given by:
\[ F = I_A L B \sin \theta \]
Since the angle \( \theta \) between the current direction and the magnetic field is \( 90^\circ \), \( \sin 90^\circ = 1 \).

Substituting the known values:
- \( I_A = 10 \, \text{A} \)
- \( L = 0.05 \, \text{m} \)
- \( B = 4.8 \times 10^{-6} \, \text{T} \)

\[ F = 10 \times 0.05 \times 4.8 \times 10^{-6} \times 1 \]
\[ F = 0.5 \times 4.8 \times 10^{-6} = 2.4 \times 10^{-6} \, \text{N} \]

### Final Answer
The force experienced by wire A due to wire B is:
\[ F = 2.4 \times 10^{-6} \, \text{N} \]

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