Two long parallel current carrying conductors 30 cm apart having current each of 10 A in opposite direction, then value of magentic field at a point of 10 cm between them, from any of the wire.

Options

A. `1xx10^(-5)T`
B. `6xx10^(-5)T`
C. `1.5xx10^(-5)T`
D. `3xx10^(-5)T`

Answer

To solve the problem, we will calculate the magnetic field at a point located 10 cm from one of the wires and 20 cm from the other wire. We will use the formula for the magnetic field due to a long straight conductor carrying current.

### Step-by-Step Solution:

1. **Identify the Configuration**:
- We have two long parallel wires, separated by a distance of 30 cm.
- Each wire carries a current of 10 A in opposite directions.
- We need to find the magnetic field at a point P, which is 10 cm from wire 1 and 20 cm from wire 2.

2. **Determine Distances**:
- Distance from wire 1 to point P (d1) = 10 cm = 0.1 m
- Distance from wire 2 to point P (d2) = 30 cm - 10 cm = 20 cm = 0.2 m

3. **Use the Formula for Magnetic Field**:
The magnetic field (B) at a distance (d) from a long straight conductor carrying current (I) is given by:
\[ B = \frac{\mu_0 I}{2 \pi d} \]
where \(\mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A}\).

4. **Calculate Magnetic Field Due to Wire 1 (B1)**:
\[ B_1 = \frac{4 \pi \times 10^{-7} \times 10}{2 \pi \times 0.1} \]
Simplifying this:
\[ B_1 = \frac{4 \times 10^{-7} \times 10}{0.2} = \frac{4 \times 10^{-6}}{0.2} = 2 \times 10^{-5} \, \text{T} \]

5. **Calculate Magnetic Field Due to Wire 2 (B2)**:
\[ B_2 = \frac{4 \pi \times 10^{-7} \times 10}{2 \pi \times 0.2} \]
Simplifying this:
\[ B_2 = \frac{4 \times 10^{-7} \times 10}{0.4} = \frac{4 \times 10^{-6}}{0.4} = 1 \times 10^{-5} \, \text{T} \]

6. **Determine the Direction of the Magnetic Fields**:
- Since the currents are in opposite directions, the magnetic fields due to each wire at point P will be in the same direction (into the page).

7. **Calculate the Net Magnetic Field (B_net)**:
\[ B_{\text{net}} = B_1 + B_2 = 2 \times 10^{-5} + 1 \times 10^{-5} = 3 \times 10^{-5} \, \text{T} \]

8. **Final Answer**:
The magnetic field at point P is \(3 \times 10^{-5} \, \text{T}\).