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 cm3.2\text{ cm} and a straight line, as shown in the above figure, is lying in a uniform magnetic field B\vec{B} of magnitude 74 mT.74\text{ mT}. The magnetic field is perpendicular to the straight line of the loop and makes an angle of 4545^\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 ms,6.0\text{ ms}, what is the approximate magnitude of the electromotive force induced in the loop during this interval?

Suppose that an elastic conducting material, which is placed in a uniform 0.800 T0.800\text{ T} magnetic field, is stretched into a circle loop with radius 15.0 cm.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 cm/s.75.0\text{ cm/s}. What is the approximate magnitude of the electromotive force induced in the shrinking loop?

A circular wire loop with radius 0.30 m0.30\text{ m} is lying in a magnetic field with magnitude 0.50 T.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 T0.20\text{ T} in 2.0 s,2.0\text{ s}, what is the approximate magnitude of the average induced electromotive force in the loop during this time interval?

Consider a conducting loop of a half-circle of radius r=0.30 m,r=0.30\text{ m}, as shown in the above figure. The loop lies in a uniform magnetic field B\vec{B} that is directed out of the screen. If the field magnitude is given by B=4.0t2+4.0t+3.0,B=4.0t^2+4.0t+3.0, where BB is in teslas and tt is in seconds, what is the approximate magnitude of the electromotive force induced around the loop by that field B\vec{B} at t=5 s?t=5\text{ s}?

A rectangular loop of wire is immersed in a nonuniform and varying magnetic field B\vec{B} that is perpendicular to and directed into the screen, as shown in the above figure. The loop has width W=3.0 mW=3.0\text{ m} and height H=2.0 m.H=2.0\text{ m}. If the magnitude of the magnetic field is given by B=5t2x2,B=5t^2x^2, where BB is in teslas, tt is in seconds, and xx is in meters, what is the magnitude of the induced electromotive force around the loop at t=0.30 s?t=0.30\text{ s}?

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