A straight, stiff wire of length 1.00 m and mass 25 g is suspended in a magnetic field B=0.75

A straight, stiff wire of length 1.00 m and mass 25 g is...

A straight, stiff wire of length $1.00 \mathrm{~m}$ and mass $25 \mathrm{~g}$ is suspended in a magnetic field $B=0.75 \mathrm{~T}$. The wire is connected to an emf. How much current must flow in the wire and in what direction so that the wire is suspended and the tension in the supporting wires is zero?

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Key Concepts

Right-Hand Rule and Current Direction

The right-hand rule is a method used to determine the direction of the magnetic force exerted on a current-carrying conductor. By pointing the fingers in the direction of the current and aligning the magnetic field using the palm’s orientation, the thumb points in the direction of the resulting force. This concept is essential to ensure that the force produced acts upward to suspend the wire.

Lorentz Force on a Current-Carrying Conductor

This concept describes how a current-carrying conductor in a magnetic field experiences a force according to the equation F = I (L x B), where I is the current, L is the length vector of the conductor, and B is the magnetic field. Understanding this force is fundamental when analyzing how electrical currents interact with magnetic fields to produce mechanical forces.

Equilibrium and Force Balance

For an object to be suspended or remain in mechanical equilibrium, the net external force acting on it must be zero. In this context, the upward magnetic force generated by the current must exactly balance the downward gravitational force (weight) of the wire. This balance allows us to determine the current required to counteract gravity.