A thin, 50.0 -cm-long metal bar with mass 750 g rests on,...

A thin, 50.0 -cm-long metal bar with mass 750 g rests on, but is not attached to, two metallic supports in a uniform $0.450 -$ T magnetic field, as shown in Fig. E27. $41 .$ A battery and a $25.0 - \Omega$ resistor in series are connected to the supports. (a) What is the highest voltage the battery can have without breaking the circuit at the supports? (b) The battery voltage has the maximum value calculated in part (a). If the resistor suddenly gets partially short-circuited, decreasing its resistance to 2.0$\Omega$ , find the initial acceleration of the bar.

A thin, 50.0 -cm-long metal bar with mass 750 g rests
on, but is not attached to, two
metallic supports in a uniform
$0.450 -$ T magnetic field, as shown
in Fig. E27. $41 .$ A battery and a
$25.0 - \Omega$ resistor in series are
connected to the supports. (a)
What is the highest voltage the battery can have without breaking the circuit at the supports?
(b) The battery voltage has the maximum value calculated in part
(a). If the resistor suddenly gets partially short-circuited, decreasing its resistance to 2.0$\Omega$ , find the initial acceleration of the bar.

Key Concepts

Ohm’s Law and Circuit Analysis

Ohm’s Law relates the voltage, current, and resistance in an electrical circuit, forming the foundation for circuit analysis. In problems where a battery supplies voltage to a resistor (and, indirectly, the moving conductor), applying Ohm’s Law helps determine the current flowing through the circuit, which in turn affects the magnitude of the induced forces and voltages.

Newton’s Second Law of Motion

Newton’s Second Law states that the acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass. This principle is crucial when connecting the electromagnetic forces, such as the Lorentz force, to the resulting mechanical acceleration of objects like a moving conductor.

Motional Electromotive Force (emf)

This concept describes how a voltage is induced in a conductor that is moving within a magnetic field. The induced emf is directly proportional to the speed of the conductor, the strength of the magnetic field, and the length of the conductor within the field. It is an essential aspect of electromagnetic induction and is governed by Faraday's law, highlighting the interplay between motion and magnetic fields.

Lorentz Force

The Lorentz force refers to the force experienced by a current-carrying conductor placed in a magnetic field. This force is perpendicular to both the direction of the current and the magnetic field, and its magnitude depends on the current, the length of the conductor within the field, and the magnetic field strength. Understanding this force is key to analyzing how electrical energy is converted into mechanical motion.

Transcript

Please give Ace some feedback