Consider a lightning bolt where 15 C of charge flows for 1500 seconds. Assume that the lightning bolt is a long, straight line current. What is the magnitude of the magnetic field at a distance of 25 m from the bolt?
To find the magnitude of the magnetic field at a distance of 25 m from the lightning bolt, we can use the Biot-Savart law. The Biot-Savart law calculates the magnetic field generated by a current-carrying wire at a specific point.
The Biot-Savart law equation is:
B = (μ₀ * I) / (2π * r)
Where:
B is the magnetic field,
μ₀ is the permeability of free space (4π × 10⁻⁷ T*m/A),
I is the current,
r is the distance from the wire.
In this case, the lightning bolt is assumed to be a long, straight current-carrying wire. Therefore, we can assume that the magnetic field will behave in a similar way.
Given:
Charge (Q) = 15 C
Time (t) = 1500 s
Current (I) = Q / t = 15 C / 1500 s = 0.01 A (Amperes)
Distance (r) = 25 m
Now we can substitute the values into the Biot-Savart law equation:
B = (μ₀ * I) / (2π * r)
B = (4π × 10⁻⁷ T*m/A * 0.01 A) / (2π * 25 m)
B = (4π × 10⁻⁷ T*m) / (2π * 25 m)
B = (2 * 10⁻⁷ T*m) / (25 m)
Now we can calculate the magnitude of the magnetic field B:
B = (2 * 10⁻⁷ T*m) / (25 m)
B = 8 × 10⁻⁹ T
Therefore, the magnitude of the magnetic field at a distance of 25 m from the lightning bolt is 8 × 10⁻⁹ Tesla (T).
To determine the magnitude of the magnetic field at a distance of 25 m from the bolt, we can use Ampere's Law. Ampere's Law states that the integral of the magnetic field dotted with the differential path length around a closed loop is equal to the product of the permeability of free space (μ₀) and the total enclosed current (I_enc).
Mathematically, it can be represented as:
∮ B · dl = μ₀ * I_enc
Since the lightning bolt is a long, straight line current, we can consider a circular loop centered around the bolt at a distance of 25 m. To simplify the calculation, let's assume a radius of 25 m, so the circumference of the loop (C) is 2π(25) = 50π m.
The total enclosed current (I_enc) is given as 15 C, which flows for 1500 seconds. Therefore, the average current can be calculated as: I = 15 C / 1500 s = 0.01 A.
Now, we can rewrite Ampere's Law as:
B * C = μ₀ * I_enc
Plugging in the values we have:
B * 50π m = (4π × 10⁻⁷ T m/A) * 0.01 A
Simplifying the equation:
B = (4π × 10⁻⁷ T m/A * 0.01 A) / (50π m)
B = (4 × 10⁻⁹ T) / (50)
B ≈ 8 × 10⁻¹¹ T
Therefore, the magnitude of the magnetic field at a distance of 25 m from the bolt is approximately 8 × 10⁻¹¹ Tesla.
currrent= 15/1500 amps
B= mu*I/2PI*current