The Magnetic Field from a Lightning Bolt. Lightning bolts...

The Magnetic Field from a Lightning Bolt. Lightning bolts can carry currents up to approximately 20 kA. We can model such a current as the equivalent of a very long, straight wire. (a) If you were unfortunate enough to be $5.0 \mathrm{~m}$ away from such a lightning bolt, how large a magnetic field would you experience? (b) How does this field compare to one you would experience by being $5.0 \mathrm{~cm}$ from a long, straight household current of $10 \mathrm{~A}$ ?

Key Concepts

Magnetic Field of a Long Straight Conductor

This concept describes the magnetic field generated by a current flowing through an infinitely long, straight wire. The field at a distance from the wire is given by the formula B = (?0 × I) / (2? × r), where I is the current and r is the distance from the wire. This relationship, derived from Ampere’s law or the Biot–Savart law, underpins the analysis of the magnetic field due to both large-scale currents like lightning and smaller, everyday currents.

Ampere’s Law

Ampere’s law is a fundamental tool in electromagnetism used to calculate the magnetic field generated by electric currents. It relates the integrated magnetic field around a closed loop to the electric current passing through the loop. This law is particularly useful in situations with high symmetry, such as with a long straight conductor, and forms the basis for deriving the magnetic field expression applicable in the problem.

Permeability of Free Space (?0)

The permeability of free space, denoted as ?0, is a constant that characterizes the ability of a vacuum to support a magnetic field. It appears in the formula for the magnetic field generated by a current (B = ?0 I / 2?r) and has a value of approximately 4? × 10^-7 T·m/A. Understanding ?0 is essential for accurately calculating and comparing magnetic fields in different scenarios.

Inverse Distance Dependence of Magnetic Fields

This concept highlights that the strength of the magnetic field generated by a current-carrying conductor decreases inversely with the distance from the wire. In practical terms, doubling the distance from the current source halves the magnetic field strength. This scaling law is critical when comparing the effects of different currents and distances, such as between a high current at a distant point and a low current at a closer proximity.

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