In a lightning bolt, a large amount of charge flows during a time of 2.2 10-3 s. Assume that the bolt can be treated as a long, straight line of current. At a perpendicular distance of 28 m from the bolt, a magnetic field of 7.3 10-5 T is measured. How much charge has flowed during the lightning bolt? Ignore the earth's magnetic field.
I thought I had to solve for I using B = mu*I/2pi*r and then figure out the current but I am stuck now. Please help
B=U•I/2π•r
I=B•2π•r/U
Once you solve for I then we use the I=Q/T formula
Q=I•T
thanks!
To solve this problem, you can use the formula for the magnetic field created by a long, straight current-carrying wire:
B = (μ0 * I) / (2π * r),
where B is the magnetic field at a perpendicular distance from the wire, I is the current flowing through the wire, μ0 is the permeability of free space (μ0 = 4π × 10^-7 T·m/A), and r is the distance from the wire.
In this case, you are given the magnetic field B = 7.3 × 10^-5 T and the distance from the bolt r = 28 m. You need to solve for the current I.
Rearranging the formula, you get:
I = (B * 2π * r) / μ0.
Substituting the given values, you have:
I = (7.3 × 10^-5 T * 2π * 28 m) / (4π × 10^-7 T·m/A).
Simplifying and canceling out units, you get:
I = 132 A.
Now that you know the current flowing through the wire is 132 A, you can find the amount of charge that has flowed during the lightning bolt using the formula:
Q = I * t,
where Q is the amount of charge, I is the current, and t is the time.
In this case, you are given the time t = 2.2 × 10^-3 s. Substituting the values, you have:
Q = 132 A * 2.2 × 10^-3 s.
Simplifying the calculation, you get:
Q = 290.4 C.
Therefore, during the lightning bolt, approximately 290.4 Coulombs of charge have flowed.
B= μ₀•I/2π•d= μ₀•q•t/2π•d
q=2π•d•B/ μ₀•t=
=2π•28•7.3•10⁻⁵/4π•10⁻⁷•2.2•10⁻³=4.64•10⁶ C