Find the magnetic field at a distance 5 cm away from a long straight wire carrying current 10 ampere 

To find the magnetic field at a distance from a long, straight current-carrying wire, you can use **Ampère's Law** or the **Biot-Savart Law**. However, the magnetic field around a long straight wire is most commonly calculated using the following formula derived from Ampère's Law:

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

where:
- \(B\) is the magnetic field at a distance \(r\) from the wire,
- \(\mu_0\) is the permeability of free space (vacuum permeability), with a value of \(\mu_0 = 4\pi \times 10^{-7} \, \text{T m/A}\),
- \(I\) is the current flowing through the wire,
- \(r\) is the distance from the wire.

### **Given Data:**
- \(I = 10 \, \text{A}\) (current in the wire),
- \(r = 5 \, \text{cm} = 0.05 \, \text{m}\) (distance from the wire).

### **Calculation:**

\[
B = \frac{\mu_0 I}{2 \pi r} = \frac{(4\pi \times 10^{-7} \, \text{T m/A}) \times 10 \, \text{A}}{2 \pi \times 0.05 \, \text{m}}
\]

Simplifying the expression:

\[
B = \frac{4\pi \times 10^{-6} \, \text{T m}}{2\pi \times 0.05 \, \text{m}}
\]

\[
B = \frac{4 \times 10^{-6} \, \text{T m}}{0.1 \, \text{m}} = 4 \times 10^{-5} \, \text{T}
\]

\[
B = 40 \, \mu\text{T}
\]

### **Final Answer:**
The magnetic field at a distance of 5 cm away from the wire carrying a current of 10 amperes is **40 microteslas (40 μT)**.

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Would you like more details on how this formula is derived or applied in different contexts?

Here are 5 related questions you might find interesting:
1. How does the magnetic field vary with distance from the wire?
2. What happens to the magnetic field if the current in the wire is doubled?
3. Can you calculate the force between two parallel current-carrying wires using the magnetic field?
4. How would the magnetic field change if the wire was not infinitely long?
5. What is the direction of the magnetic field around a current-carrying wire, and how can you determine it?

**Tip**: The right-hand rule is a useful tool for determining the direction of the magnetic field around a current-carrying conductor.

Learn how to calculate the magnetic field at a distance of 5 cm from a long straight wire carrying 10 amperes of current. Includes detailed step-by-step solution using Ampère's Law and Biot-Savart Law, with a final result of 40 microteslas (40 μT).

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