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College Physics (Urone)
Found in: Page 861
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

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 \({\rm{10}}{\rm{.0 ms}}\)?

Electromotive force is \({\rm{157 mV}}\).

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Definition of electromotive force

Electromotive force is defined as the electric potential produced by either an electrochemical cell or by changing the magnetic field. EMF is the commonly used acronym for electromotive force.

A generator or a battery is used for the conversion of energy from one form to another. In these devices, one terminal becomes positively charged while the other becomes negatively charged. Therefore, an electromotive force is work done on a unit electric charge.

Step 2: Calculate the electromotive force.

The electromotive force is given by

\({\rm{\varepsilon }} = - {\rm{N}}\frac{{{\rm{\Delta \Phi }}}}{{{\rm{\Delta t}}}}\)

\({\rm{\Phi }} = {\rm{BAcos(\theta )}}\) is the flux, thus the change from when the coil is perpendicular to the magnetic field until it is parallel will just be \({\rm{\Delta \Phi }} = {\rm{AB}}\).

Therefore, we have

\({\rm{\varepsilon }} = - \left( {\frac{{{\rm{NAB}}}}{{\rm{t}}}} \right)\)

where \(t\) is the time for the needed change in the flux, given in the exercise. Numerically, neglecting the minus in the formula, we will have

\(\begin{aligned}{}{\rm{\varepsilon }} &= \frac{{{\rm{1000}} \times \left( {{\rm{\pi }} \times \frac{{{{\left( {{\rm{0}}{\rm{.2}}\;{\rm{m}}} \right)}^{\rm{2}}}}}{4}} \right) \times \left( {{\rm{5}}{\rm{.00}} \times {\rm{1}}{{\rm{0}}^{{\rm{ - 5}}}}\;T} \right)}}{{{\rm{10}}{\rm{.0}}\;{\rm{ms}}\left( {\frac{{{\rm{1}}{{\rm{0}}^{{\rm{ - 3}}}}\;s}}{{1\;{\rm{ms}}}}} \right)}}\\ &= {\rm{157}} \times {\rm{1}}{{\rm{0}}^{{\rm{ - 3}}}}\;{\rm{V}}\left( {\frac{{{\rm{1}}\;mV}}{{{\rm{1}}{{\rm{0}}^{{\rm{ - 3}}}}\;V}}} \right)\\ &= 157\;mV\end{aligned}\)

Hence, the electromotive force is \({\rm{157}}\;{\rm{mV}}\).

Most popular questions for Physics Textbooks

The Tethered Satellite discussed in this module is producing 5.00 kV, and a current of 10.0 A flows. (a) What magnetic drag force does this produce if the system is moving at 7.80 km/s? (b) How much kinetic energy is removed from the system in 1.00 h, neglecting any change in altitude or velocity during that time? (c) What is the change in velocity if the mass of the system is 100,000 kg? (d) Discuss the long-term consequences (say, a week-long mission) on the space shuttle’s orbit, noting what effect a decrease in velocity has and assessing the magnitude of the effect.

A \(500\)-turn coil with a\(0.250{\rm{ }}{m^2}\)area is spun in the Earth’s \(5.00 \times {10^{ - 5}}{\rm{ }}T\) field, producing a \(12.0{\rm{ }}kV\) maximum emf.

(a) At what angular velocity must the coil be spun?

(b) What is unreasonable about this result?

(c) Which assumption or premise is responsible?

(a) An MRI technician moves his hand from a region of very low magnetic field strength into an MRI scanner’s 2.00 T field with his fingers pointing in the direction of the field. Find the average emf induced in his wedding ring, given its diameter is 2.20 cm and assuming it takes 0.250 s to move it into the field. (b) Discuss whether this current would significantly change the temperature of the ring.

A plug-in transformer, like that in Figure \(23.29\), supplies \(9.00{\rm{ }}V\) to a video game system.

(a) How many turns are in its secondary coil, if its input voltage is \(120{\rm{ }}V\) and the primary coil has \(400\) turns?

(b) What is its input current when its output is \(1.30{\rm{ }}A\)?

A person who works with large magnets sometimes places her head inside a strong field. She reports feeling dizzy as she quickly turns her head. How might this be associated with induction?
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