A 1.6-m length of wire carrying 4.5 A of current toward the...

A 1.6-m length of wire carrying 4.5 A of current toward the south is oriented horizontally. At that point on the Earth's surface, the dip angle of the Earth's magnetic field makes an angle of $41^{\circ}$ to the wire. Estimate the magnitude of the magnetic force on the wire due to the Earth's magnetic field of $5.5 \times 105 \mathrm{~T}$ at this point.

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Key Concepts

Magnetic Force on a Current-Carrying Conductor

This concept describes how a wire carrying an electric current experiences a force when placed in a magnetic field. The force is given by the formula F = I L B sin?, where I is the current through the wire, L is the length of the wire exposed to the field, B is the magnetic field strength, and ? is the angle between the direction of current and the magnetic field. This relationship is derived from the Lorentz force law and shows that the maximum force occurs when the current and field are perpendicular.

Dip Angle of the Earth's Magnetic Field

The dip angle refers to the angle between the Earth's magnetic field lines and the horizontal plane. It indicates the extent to which the magnetic field is inclined relative to the surface of the Earth. In problems involving the interaction between a current-carrying conductor and the Earth's magnetic field, the dip angle is used to determine the effective component of the magnetic field that is perpendicular to the conductor, which directly affects the magnitude of the force experienced.

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