Consider the circuit shown in Fig. E29.29, but with the bar...

Consider the circuit shown in Fig. E29.29, but with the bar moving to the right with speed $v .$ As in Exercise $29.29,$ the bar has length $0.360 \mathrm{~m}, R=45.0 \Omega,$ and $B=0.650 \mathrm{~T}$. (a) Is the induced current in the circuit clockwise or counterclockwise? (b) At an instant when the $45.0 \Omega$ resistor is dissipating electrical energy at a rate of $0.840 \mathrm{~J} / \mathrm{s},$ what is the speed of the bar?

Key Concepts

Electromagnetic Induction

This concept describes the process by which a changing magnetic environment, such as that produced by a moving conductor in a magnetic field, induces an electromotive force (emf) in a circuit. It is a fundamental principle that explains how mechanical motion can be converted into electrical energy.

Faraday’s Law

Faraday’s law quantifies the induced emf in a circuit based on the rate of change of magnetic flux. When the area of the circuit changes because a component moves through a magnetic field, the resulting change in flux determines the magnitude of the induced emf.

Lenz’s Law

Lenz’s law provides the direction of the induced current resulting from a change in magnetic flux. It states that the induced current will flow in a direction such that its own magnetic field opposes the change that produced it, thereby ensuring the conservation of energy.

Motional EMF

Motional emf is generated when a conductor moves through a magnetic field. The emf produced is directly proportional to the speed of the conductor, the magnetic field strength, and the effective length of the conductor within the field, linking mechanical motion to electrical output.

Power Dissipation in Resistors

This concept refers to the conversion of electrical energy into heat in a resistor. The power dissipated in a resistor is given by formulas like P = I^2R or P = V^2/R, which connect the induced emf and current in the circuit to observable energy losses.

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