A 2.60 -N metal bar, 1.50 m long and having a resistance of 10.0Ω, rests horizontally on conduc

step 1 We'll use the equation of force exerted by the magnetic field on the conductor bar of length, ki

A 2.60 -N metal bar, 1.50 m long and having a resistance of...

A 2.60 -N metal bar, 1.50$\mathrm { m }$ long and having a resistance of 10.0$\Omega$ , rests horizontally on conducting wires connecting it to the circuit shown in Fig. P27.70. The bar is in a uniform, horizontal, 1.60 -T magnetic field and is not attached to the wires in the circuit. What is the acceleration of the bar just after the switch $S$ is closed?

A 2.60 -N metal bar, 1.50$\mathrm { m }$ long and having a resistance of 10.0$\Omega$ , rests horizontally on conducting wires connecting
it to the circuit shown in Fig. P27.70. The bar is in a uniform, horizontal, 1.60 -T magnetic field and is not attached to the wires in the
circuit. What is the acceleration of the bar just after the switch $S$ is
closed?

Key Concepts

Magnetic Force on a Current?Carrying Conductor

This concept describes how a conductor carrying an electric current experiences a force when placed in a magnetic field. The force, often called the Lorentz force, is given by F = I·L·B when the current I, the length L of the conductor, and the magnetic field B are mutually perpendicular. It is the key principle that explains how electromagnetic forces produce motion in conductors, which is central to many applications in electromechanics.

Ohm's Law

Ohm’s Law is a fundamental principle that relates the voltage across a conductor to the current flowing through it and the resistance it offers, expressed as I = V/R. In contexts where a current flows through a circuit, this law is used to determine the magnitude of the current based on the applied voltage and the circuit’s resistance, which is essential for calculating the resulting magnetic force.

Newton's Second Law of Motion

Newton’s Second Law states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass (F = m·a). This principle is used to determine the acceleration of an object when the net electromagnetic force (as determined from the current and magnetic field) and the object's mass are known.

Conversion from Weight to Mass

In many physics problems, the weight of an object is given instead of its mass. Weight is the force exerted on an object due to gravity and is calculated as W = m·g. To apply Newton’s Second Law, the mass is needed, which is obtained by dividing the weight by the gravitational acceleration (g). This conversion is crucial when analyzing the motion resulting from forces.

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