A straight, 2.00 -m, 150-g wire carries a current in a...

A straight, 2.00 -m, $150-\mathrm{g}$ wire carries a current in a region where the earth's magnetic field is horizontal with a magnitude of 0.55 gauss. (a) What is the minimum value of the current in this wire so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it? Does it seem likely that such a wire could support this size of current? (b) Show how the wire would have to be oriented relative to the earth's magnetic field to be supported in this way.

Key Concepts

Lorentz Force on a Current-Carrying Conductor

This concept explains that a current-carrying wire in a magnetic field experiences a force, given by the equation F = I L B sin?, where I is the current in the wire, L is the length of the wire, B is the magnetic field strength, and ? is the angle between the wire and the magnetic field. This force arises due to the interaction between the moving charges in the conductor and the magnetic field, and its magnitude depends on how the conductor is oriented relative to the magnetic field.

Weight and Force Equilibrium

This concept involves setting the upward magnetic force equal to the downward gravitational force (weight) to achieve support or equilibrium. Weight is calculated as mg, where m is the mass and g is the acceleration due to gravity. In problems like this, finding the current that makes the magnetic force equal to the weight helps confirm whether the magnetic force can fully support the object.

Magnetic Field Measurement and Unit Conversion

Many problems involve practical measurements of magnetic field strength in units like gauss or tesla. Understanding the conversion between these units (1 gauss = 10^-4 tesla) is essential because the proper unit must be used in calculations involving physical laws such as the Lorentz force equation.

Vector Cross Product and Orientation

The force on a current-carrying wire is determined by the vector cross product of the current direction and the magnetic field, which offers insight into the force’s direction. Maximizing the force requires orienting the wire such that it is perpendicular to the magnetic field (? = 90°), ensuring sin? is maximized. Understanding this vector relationship is crucial in determining the appropriate orientation of the wire relative to the magnetic field for optimal force direction.

Transcript

Please give Ace some feedback