(II) A power line carries a current of 95 A west along the...

(II) A power line carries a current of 95 A west along the tops of 8.5-m-high poles. ($a$) What is the magnitude and direction of the magnetic field produced by this wire at the ground directly below? How does this compare with the Earth's magnetic field of about $\frac{1}{2}$G? ($b$) Where would the wire's magnetic field cancel the Earth's field?

Key Concepts

Earth’s Magnetic Field

Earth’s magnetic field, typically on the order of 0.5 Gauss, represents the natural geomagnetic field in the vicinity of the planet’s surface. Knowledge of its magnitude and direction is important when comparing it to locally produced magnetic fields, such as that from power lines, to understand possible interactions and resultant effects like field cancellation or reinforcement.

Superposition Principle in Magnetism

The superposition principle states that when multiple magnetic fields are present, the total magnetic field at any point is the vector sum of the individual fields. This concept is critical when analyzing scenarios where the magnetic field produced by a current-carrying conductor interacts with the Earth’s magnetic field, leading to cancellation points where the net field becomes zero.

Magnetic Field of a Current?Carrying Conductor

This concept involves using the well-known formula B = ?0I/(2?r) to compute the magnetic field produced by a long, straight conductor carrying an electric current. It is based on Ampère’s law and the Biot–Savart law, where ?0 is the permeability of free space, I is the current, and r is the radial distance from the wire. This formula is essential for determining the strength of the magnetic field at any specified distance from a conductor.

Right?Hand Rule

The right-hand rule is a crucial method for determining the direction of the magnetic field around a current-carrying wire. By aligning the thumb of the right hand with the direction of the conventional current, the direction in which the fingers curl indicates the direction of the magnetic field lines. This spatial relationship is fundamental for understanding the orientation of fields in electromagnetic problems.

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