Electricity and Magnetism

Magnetic Flux, Induction, and Ampere's Circuital Law

Magnetic flux and Faraday's law (quantitative)

         

A closed loop of wire that consists of a semicircle of radius \(3.2\text{ cm}\) and a straight line, as shown in the above figure, is lying in a uniform magnetic field \(\vec{B}\) of magnitude \(74\text{ mT}.\) The magnetic field is perpendicular to the straight line of the loop and makes an angle of \(45^\circ\) with the plane of the semicircle. If the magnetic field is reduced to zero at a uniform rate during a time interval of \(6.0\text{ ms},\) what is the approximate magnitude of the electromotive force induced in the loop during this interval?

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Suppose that an elastic conducting material, which is placed in a uniform \(0.800\text{ T}\) magnetic field, is stretched into a circle loop with radius \(15.0\text{ cm}.\) The plane of the loop is perpendicular to the magnetic field, and the stretched loop is released to shrink at an instantaneous rate of \(75.0\text{ cm/s}.\) What is the approximate magnitude of the electromotive force induced in the shrinking loop?

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A circular wire loop with radius \(0.30\text{ m}\) is lying in a magnetic field with magnitude \(0.50\text{ T}.\) The plane of the loop is perpendicular to the magnetic field. If the direction of the magnetic field is reversed and its magnitude is reduced to \(0.20\text{ T}\) in \(2.0\text{ s},\) what is the approximate magnitude of the average induced electromotive force in the loop during this time interval?

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Consider a conducting loop of a half-circle of radius \(r=0.30\text{ m},\) as shown in the above figure. The loop lies in a uniform magnetic field \(\vec{B}\) that is directed out of the screen. If the field magnitude is given by \(B=4.0t^2+4.0t+3.0,\) where \(B\) is in teslas and \(t\) is in seconds, what is the approximate magnitude of the electromotive force induced around the loop by that field \(\vec{B}\) at \(t=5\text{ s}?\)

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A rectangular loop of wire is immersed in a nonuniform and varying magnetic field \(\vec{B}\) that is perpendicular to and directed into the screen, as shown in the above figure. The loop has width \(W=3.0\text{ m}\) and height \(H=2.0\text{ m}.\) If the magnitude of the magnetic field is given by \(B=5t^2x^2,\) where \(B\) is in teslas, \(t\) is in seconds, and \(x\) is in meters, what is the magnitude of the induced electromotive force around the loop at \(t=0.30\text{ s}?\)

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