a lighting bolt may carry a current of 1(10^4)A for ashort time.What is the resulting magnetic field 100 from the bolt?

To determine the magnetic field generated by a lightning bolt at a distance of 100 meters, we can use the concept of the magnetic field produced by a long, straight conductor carrying an electric current. The formula we will use is derived from Ampère's Law, which relates the magnetic field around a conductor to the current flowing through it.

Understanding the Magnetic Field Around a Current-Carrying Conductor

The magnetic field (B) around a long, straight wire carrying a current (I) can be calculated using the formula:

B = (μ₀ * I) / (2 * π * r)

Where:

• B = magnetic field strength in teslas (T)
• μ₀ = permeability of free space (approximately 4π x 10^-7 T·m/A)
• I = current in amperes (A)
• r = distance from the wire in meters (m)

Plugging in the Values

In this case, the current (I) is given as 1 x 10^4 A (or 10,000 A), and the distance (r) is 100 m. Now, we can substitute these values into the formula:

B = (4π x 10^-7 T·m/A * 10,000 A) / (2 * π * 100 m)

Calculating the Magnetic Field

Let’s simplify the equation step by step:

1. First, calculate the numerator:

4π x 10^-7 T·m/A * 10,000 A = 4 x 10^-3 T·m

2. Now, calculate the denominator:

2 * π * 100 m = 200π m

3. Now, we can substitute these results back into the equation:

B = (4 x 10^-3 T·m) / (200π m)

4. Simplifying this gives:

B ≈ (4 x 10^-3) / (628.32) T

B ≈ 6.37 x 10^-6 T

Final Result

The resulting magnetic field at a distance of 100 meters from the lightning bolt is approximately 6.37 microteslas (µT). This value illustrates how even a powerful current like that from a lightning bolt produces a relatively weak magnetic field at a distance, highlighting the rapid decrease in magnetic field strength with distance from the source.

Real-World Implications

This calculation is not just theoretical; it has practical implications in fields like meteorology and electrical engineering. Understanding the magnetic fields generated by lightning can help in designing better lightning protection systems and in studying the effects of lightning on the environment.