It may be desirable to increase the maximum induced current...

It may be desirable to increase the maximum induced current in the brain tissue. In $\textbf{Fig. P29.73}$, which time-dependent graph of the magnetic field $B$ in the coil achieves that goal? Assume that everything else remains constant. (a) A; (b) B; (c) either A or B; (d) neither A nor B.

Key Concepts

Electromagnetic Induction

This fundamental concept describes the process by which a changing magnetic field creates an induced electromotive force (EMF) in a conductor. It is the basis for the operation of many electrical devices and explains how electrical currents can be generated without direct contact.

Faraday's Law of Induction

Faraday's Law quantifies electromagnetic induction by stating that the induced EMF in a coil is proportional to the rate of change of magnetic flux through the coil. It emphasizes that a faster change in magnetic flux (or magnetic field strength) results in a larger induced voltage, which in turn can produce a higher current if other factors are kept constant.

Rate of Change of Magnetic Field

This concept is central to understanding how variations in a magnetic field affect induced currents. A more rapid change or a steeper slope in the graph of the magnetic field over time leads to a higher rate of change, thereby increasing the magnitude of the induced EMF and the resulting current in the tissue or conductor.

Time-dependent Magnetic Field Graphs

Graphical representations of magnetic fields over time allow us to visually compare how quickly the field changes. The steeper the slope on such a graph, the greater the instantaneous rate of change, which according to Faraday’s Law, corresponds to a larger induced EMF. This concept highlights the importance of temporal characteristics in the design of systems that rely on electromagnetic induction.

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