A 13.0 g wire of length L=62.0 cm is suspended by a pair of flexible leads in a uniform magnet

step 1 In this question, we have this setup. So we have a wire that is being supported by two springs.

A 13.0 g wire of length L=62.0 cm is suspended by a pair...

A $13.0 \mathrm{~g}$ wire of length $L=62.0 \mathrm{~cm}$ is suspended by a pair of flexible leads in a uniform magnetic field of magnitude $0.440 \mathrm{~T}$ (Fig. $28-41$ ). What are the (a) magnitude and (b) direction (left or right) of the current required to remove the tension in the supporting leads?

Key Concepts

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the force experienced by a current-carrying conductor in a magnetic field. By orienting the thumb in the direction of the current and the fingers in the direction of the magnetic field, the resultant force is indicated by the direction in which the palm pushes. This rule is fundamental in electromagnetism for predicting the behavior of conductors in magnetic fields.

Gravitational Force

Gravitational force is the weight of an object, which is calculated using the equation W = mg, where m is the mass and g is the acceleration due to gravity. This force acts downward and must be counteracted by other forces in order to achieve equilibrium. In problems involving suspended objects, such as wires in a magnetic field, the gravitational force is a key factor in determining the conditions for balance.

Magnetic Force on a Current-Carrying Conductor

This concept involves the understanding that a current-carrying conductor placed in a magnetic field experiences a force. The magnitude of this force is given by the equation F = I L B sin?, where I is the current, L is the length of the conductor within the field, B is the magnetic field strength, and ? is the angle between the direction of the current and the magnetic field. This principle is a core part of electromagnetism and is essential for analyzing interactions in devices like motors and generators.

Equilibrium of Forces

In many physical scenarios, objects remain at rest when the sum of the forces acting upon them is zero. In the context of the problem, this principle is applied by ensuring that the upward magnetic force exactly balances the downward gravitational force (weight) on the object. Understanding force equilibrium is crucial for designing systems where stability is required and is widely used in static and dynamic analysis.

Transcript

Please give Ace some feedback