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College Physics (Urone)
Found in: Page 860
College Physics (Urone)

College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

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Short Answer

An \({\rm{emf}}\) is induced by rotating a \({\rm{1000 - }}\)turn, \({\rm{20}}{\rm{.0 cm}}\) diameter coil in the Earth’s \({\rm{5}}{\rm{.00 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{ T}}\) magnetic field. What average \({\rm{emf}}\) is induced, given the plane of the coil is originally perpendicular to the Earth’s field and is rotated to be parallel to the field in\({\rm{10}}{\rm{.0 ms}}\)?

The average \({\rm{emf}}\) induced is obtained as \({\rm{1}}{\rm{.57}}\;{\rm{mV}}\).

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Define Electromagnetic Induction

The creation of an electromotive force across an electrical conductor in a changing magnetic field is known as electromagnetic or magnetic induction. Induction was discovered in \({\rm{1831}}\) by Michael Faraday, and it was mathematically characterized as Faraday's law of induction by James Clerk Maxwell.

Step 2: Evaluating the average emf induced

The electromotive force is induced when a coil with the value \({\rm{N}}\) turns experiences a flux change of the value \({\rm{\Delta \Phi }}\) in time \({\rm{\Delta t}}\) is given by:

\({\rm{E = - N}}\frac{{{\rm{\Delta \Phi }}}}{{{\rm{\Delta t}}}}\)……………….(1)

The flux reaches the point zero from the maximal value under the given time, we can simply write the change in flux as:

\(\begin{aligned}{}{\rm{\Delta \Phi = 0 - BA}}\\{\rm{ = - BA}}\end{aligned}\)

The emf then will be:

\({\rm{\varepsilon = }}\frac{{{\rm{NBA}}}}{{\rm{t}}}\)……………………….(2)

Substituting the area such that:

\(\begin{aligned}{}{\rm{A = \pi }}{{\rm{R}}^{\rm{2}}}\\{\rm{ = }}\frac{{{\rm{\pi }}{{\rm{D}}^{\rm{2}}}}}{{\rm{4}}}\end{aligned}\)

Therefore the analytical result is,

\({\rm{\varepsilon = }}\frac{{{\rm{\pi NB}}{{\rm{D}}^{\rm{2}}}}}{{\rm{4}}}\)………………………(3)

The numerical value is then evaluated as:

\(\begin{aligned}{}{\rm{\varepsilon }} &= \frac{{{\rm{\pi \times 1000 \times }}\left( {{\rm{5 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}\;{\rm{T}}} \right){\rm{ \times }}{{\left( {{\rm{0}}{\rm{.2}}\;{\rm{m}}} \right)}^{\rm{2}}}}}{{\rm{4}}}\\ &= {\rm{1}}{\rm{.57\;}} \times {\rm{1}}{{\rm{0}}^{ - {\rm{3}}}}\;{\rm{V}}\left( {\frac{{1\;{\rm{mV}}}}{{{\rm{1}}{{\rm{0}}^{ - {\rm{3}}}}\;{\rm{V}}}}} \right)\\ &= {\rm{1}}{\rm{.57}}\;{\rm{mV}}\end{aligned}\)

Therefore, the average \({\rm{emf}}\) induced is obtained as \({\rm{1}}{\rm{.57}}\;{\rm{mV}}\).

Most popular questions for Physics Textbooks

Referring to Example 23.14, find the average power at \({\rm{10}}{\rm{.0}}\;{\rm{kHz}}\).

What is the peak emf generated by rotating a 1000-turn, \({\rm{5}}{\rm{.00 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{ T}}\) diameter coil in the Earth’s magnetic field, given the plane of the coil is originally perpendicular to the Earth’s field and is rotated to be parallel to the field in \({\rm{10}}{\rm{.0 ms}}\)?

High-frequency noise in AC power can damage computers. Does the plug-in unit designed to prevent this damage use a large inductance or a large capacitance (in series with the computer) to filter out such high frequencies? Explain.

A large research solenoid has a self-inductance of 25.0 H (a) What induced emf opposes shutting it off when 100 A of current through it is switched off in 80.0 ms? (b) How much energy is stored in the inductor at full current? (c) At what rate in watts must energy be dissipated to switch the current off in 80.0 ms? (d) In view of the answer to the last part, is it surprising that shutting it down this quickly is difficult?

At what angular velocity in rpm will the peak voltage of a generator be \(480V\), if its \(500\)-turn, \(8.00cm\) diameter coil rotates in a \(0.250T\) field?
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