In a lightning bolt, 16 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 24 m from the bolt?
To find the magnitude of the magnetic field at a distance of 24 m from the bolt, we can use Ampere's Law.
Ampere's Law states that the line integral of the magnetic field around a closed loop is equal to the product of the current passing through the loop and the permeability of free space (μ₀).
The equation for Ampere's Law is given by:
∮ B · dl = μ₀ * I,
where B is the magnetic field, dl is an infinitesimally small length element along the loop, I is the current passing through the loop, and ∮ denotes a closed line integral.
In this case, we can consider a circular loop of radius r = 24 m centered around the lightning bolt. The line integral of the magnetic field along this loop is equivalent to B multiplied by the circumference of the loop.
∮ B · dl = B * 2πr.
The current passing through the loop, I, is given as 16 C (coulombs) flowing in a time of 1.5 * 10⁻³ s (seconds). Current is defined as the rate of flow of charge, so we can calculate the value of I as follows:
I = q / t,
where q is the charge and t is the time.
Plugging in the given values, we have:
I = 16 C / 1.5 * 10⁻³ s.
Now, we can substitute the values into Ampere's Law equation:
B * 2πr = μ₀ * I.
Next, we rearrange the equation to solve for B:
B = (μ₀ * I) / (2πr).
Finally, we substitute the known values:
B = (μ₀ * (16 C / 1.5 * 10⁻³ s)) / (2π * 24 m).