Magnetic force on a lightning bolt. Currents during...

Magnetic force on a lightning bolt. Currents during lightning strikes can be up to $50,000$ A (or more!). We can model such a strike as a $50,000$ A vertical current perpendicular to the earth's magnetic field, which is about $\frac{1}{2}$ gauss. What is the force on each meter of this current due to the earth's magnetic field?

Key Concepts

Cross Product and Perpendicular Orientation

The cross product in the formula F = I (L x B) shows that the force is maximized when the current-carrying conductor is oriented perpendicular to the magnetic field. This concept highlights the importance of the geometric relationship between the direction of the current and the magnetic field in determining both the magnitude and direction of the resulting force.

Magnetic Field and Unit Conversion

A magnetic field is a vector field that represents the magnetic influence exerted by moving electric charges and magnetic materials. In physics, it is typically measured in tesla (T) in the International System of Units, although other units such as gauss are also used (noting that 1 T equals 10,000 gauss). Understanding these units and how to convert between them is essential when analyzing electromagnetic phenomena.

Magnetic Force on a Current-Carrying Conductor

This concept explains that a conductor carrying an electric current in the presence of a magnetic field experiences a force. This force is quantified by the equation F = I (L x B), indicating that the magnitude of the force depends on the current, the length of the conductor, and the magnetic field strength, as well as the sine of the angle between the current direction and the magnetic field.

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