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Electricity and Magnetism

Magnetic Flux, Induction, and Ampere's Circuital Law

Excel in math and science

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Concept Quizzes

Ampere's law (Quantitative)
Using Magnetic Flux/Faraday's Law
Lenz's Law
Magnetic Moment

Challenge Quizzes

Level 4-5

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?

\[ 0.7\times 10^{-2}\text{ V} \] \[ 2.8\times 10^{-2}\text{ V} \] \[ 2.1\times 10^{-2}\text{ V} \] \[ 1.4\times 10^{-2}\text{ V} \]

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by Brilliant Staff

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?

\( 1.131\text{ V} \) \( 0.565\text{ V} \) \( 1.696\text{ V} \) \( 0.283\text{ V} \)

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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?

\( 99.0\text{ mV} \) \( 39.6\text{ mV} \) \( 59.4\text{ mV} \) \( 79.2\text{ mV} \)

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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 \(t=5\text{ s}?\)

\[ 1.6\text{ V} \] \[ 6.2\text{ V} \] \[ 3.1\text{ V} \] \[ 0.6\text{ V} \]

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by Brilliant Staff

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 \(t=0.30\text{ s}?\)

\( 54.0\text{ V} \) \( 40.5\text{ V} \) \( 13.5\text{ V} \) \( 27.0\text{ V} \)

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by Brilliant Staff

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 5 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Magnetic Flux, Induction, and Ampere's Circuital Law

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 5 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Concept Quizzes

Challenge Quizzes

Magnetic flux and Faraday's law (quantitative)

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.