In a lightning bolt, 13 C of charge flows in a time of 1.5*10-3 s. Assuming that the lightning bolt can be represented as a long, straight line of current, what is the magnitude of the magnetic field at a distance of 29 m from the bolt?
The current is
I = Q/(time) = 13/1.5*10^-3s = 8670 Amps
Use the formula for the B-field around an infinite linear current at distance R.
B = mu* I/(2 pi R)
Where mu is the permeabilty of free space.
To calculate the magnitude of the magnetic field at a distance of 29 m from the lightning bolt, we can use the formula for calculating the magnetic field created by a long, straight line current.
The formula is given by:
B = (μ₀ * I) / (2π * r)
Where:
B is the magnitude of the magnetic field
μ₀ is the permeability of free space, which has a value of 4π x 10⁻⁷ T m/A
I is the current
r is the distance from the lightning bolt
First, let's calculate the current in amperes. The given value is 13 C of charge in a time of 1.5 x 10⁻³ s. The equation for current is I = Q / t, where Q is the charge and t is the time.
I = 13 C / 1.5 x 10⁻³ s
I = 8666.67 A (rounded to the nearest whole number)
Now we can substitute the values into the formula to calculate the magnetic field:
B = (4π x 10⁻⁷ T m/A * 8666.67 A) / (2π * 29 m)
B = (2.73 x 10⁻² T m) / (58 m)
B ≈ 4.72 x 10⁻⁴ T
Therefore, the magnitude of the magnetic field at a distance of 29 m from the lightning bolt is approximately 4.72 x 10⁻⁴ Tesla.