Final answer:
The force per meter on the lightning bolt is 0.609 N/m, and the direction of the force, determined by the right-hand rule, is due east if the lightning bolt's current is straight up and the Earth's field direction is due north.
Step-by-step explanation:
To calculate the force per meter on a lightning bolt at the equator that carries a current perpendicular to the Earth's magnetic field, we use the formula F = ILB sin(θ), where F stands for force, I is the current in amperes, L is the length in meters over which the force acts, B is the magnetic field strength in teslas, and θ is the angle between the current direction and the magnetic field.
Given that the lightning bolt carries 20,300 A and the Earth's magnetic field strength at the equator is 3.00 × 10⁻⁵ T, and the angle θ is 90 degrees since the current is perpendicular to the field:
F = (20,300 A)(1 m)(3.00 × 10⁻⁵ T) sin(90°)
F = 20,300 A × 3.00 × 10⁻⁵ T
F = 0.609 N/m
The direction of the force would be perpendicular to both the current flow and the magnetic field direction, which is determined by the right-hand rule. Here, if the lightning bolt's current is straight up and the magnetic field direction is due north, the force acts due east.