Calculate the magnetic field at a point P. `0.5 `m away from an infinitely long straight wire carrying current of 90 A.

Answer

To calculate the magnetic field at a point P, which is 0.5 m away from an infinitely long straight wire carrying a current of 90 A, we can use the formula derived from Ampère's circuital law or the Biot-Savart law. The magnetic field (B) at a distance (d) from a long straight wire carrying current (I) is given by the formula:

\[ B = \frac{\mu_0 I}{2 \pi d} \]

Where:
- \( B \) is the magnetic field,
- \( \mu_0 \) is the permeability of free space, approximately \( 4\pi \times 10^{-7} \, \text{T m/A} \),
- \( I \) is the current in amperes,
- \( d \) is the distance from the wire in meters.

### Step-by-step Solution:

1. **Identify the given values:**
- Current, \( I = 90 \, \text{A} \)
- Distance, \( d = 0.5 \, \text{m} \)

2. **Substitute the values into the formula:**
\[ B = \frac{\mu_0 I}{2 \pi d} \]
Substituting \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \):
\[ B = \frac{(4\pi \times 10^{-7}) \times 90}{2 \pi \times 0.5} \]

3. **Simplify the equation:**
- The \( \pi \) in the numerator and denominator cancels out:
\[ B = \frac{4 \times 10^{-7} \times 90}{2 \times 0.5} \]
- Simplifying further:
\[ B = \frac{4 \times 10^{-7} \times 90}{1} = 4 \times 10^{-7} \times 90 \]

4. **Calculate the value:**
\[ B = 360 \times 10^{-7} \, \text{T} = 3.6 \times 10^{-5} \, \text{T} \]

5. **Final answer:**
The magnetic field at point P is:
\[ B = 3.6 \times 10^{-5} \, \text{T} \]