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College Physics (Urone)
Found in: Page 815
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 inventor wants to generate \({\rm{120 - V}}\) power by moving a \({\rm{1}}{\rm{.00 - m - long}}\) wire perpendicular to the Earth's \({\rm{5}}{\rm{.00 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{\;T}}\) field. (a) Find the speed with which the wire must move. (b) What is unreasonable about this result? (c) Which assumption is responsible?

  1. The speed with which the wire must move is \({\rm{2}}{\rm{.40 \times 1}}{{\rm{0}}^{\rm{6}}}{\rm{\;m/s}}\).
  2. Unreasonable about this result is the speed is too fast to be useful.
  3. The Earth's magnetic field is just too feeble to generate this much energy with a single \({\rm{1}}{\rm{.0 - m}}\) wire.
See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Concept Introduction

The area of space near a magnetic body or a current-carrying body where magnetic forces caused by the body or current can be detected.

Step 2: Calculate the value of speed

(a)

The energy is proportional to the strength of the magnetic field, the length of the wire, and the velocity.

\({\rm{E}} = {\rm{v}} \times {\rm{L}} \times {\rm{B}}\)

calculate this equation for the speed at which the wire must move using the parameters in question.

\(\begin{aligned}{}{\rm{v}} &= \frac{{\rm{E}}}{{{\rm{L}} \times {\rm{B}}}}\\ &= \frac{{{\rm{120}}{\rm{.0\;V}}}}{{{\rm{1}}{\rm{.00\;m}} \times \left( {{\rm{5}}{\rm{.00}} \times {\rm{1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{\;T}}} \right)}}\\ &= {\rm{2}}{\rm{.40}} \times {\rm{1}}{{\rm{0}}^{\rm{6}}}\;{\rm{m/s}}\end{aligned}\)

Therefore, the speed with which the wire must move is \({\rm{2}}{\rm{.40 \times 1}}{{\rm{0}}^{\rm{6}}}{\rm{\;m/s}}\).

Step 3: Explaining the unreasonable result

The speed is too fast to be useful; it is comparable to the speed of light (about \({\rm{1}}{\rm{.0 \% }}\) of the speed of light).

Step 4: Explaining the assumptions

(c)

The Earth's magnetic field is too weak to generate this much energy with a single \({\rm{1}}{\rm{.0}}\;{\rm{m}}\)telegraph wire.

Most popular questions for Physics Textbooks

(a) An oxygen\({\rm{ - 16}}\) ion with a mass of \({\rm{2}}{\rm{.66 \times 1}}{{\rm{0}}^{{\rm{ - 26}}}}{\rm{ kg}}\) travels at \({\rm{5}}{\rm{.00 \times 1}}{{\rm{0}}^{\rm{6}}}{\rm{ m/s}}\) perpendicular to a \({\rm{1}}{\rm{.20 - T}}\) magnetic field, which makes it move in a circular arc with a 0.231-m radius. What positive charge is on the ion? (b) What is the ratio of this charge to the charge of an electron? (c) Discuss why the ratio found in (b) should be an integer.

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What is the direction of the magnetic field that produces the magnetic force on a positive charge as shown in each of the three cases in the figure below, assuming B is perpendicular to v?

Suppose two long straight wires run perpendicular to one another without touching. Does one exert a net force on the other? If so, what is its direction? Does one exert a net torque on the other? If so, what is its direction? Justify your responses by using the right hand rules.

(a) Viewers of Star Trek hear of an antimatter drive on the Starship Enterprise. One possibility for such a futuristic energy source is to store antimatter-charged particles in a vacuum chamber, circulating in a magnetic field, and then extract them as needed. Antimatter annihilates with normal matter, producing pure energy. What strength magnetic field is needed to hold antiprotons, moving at \({\rm{5}}{\rm{.00 \times 1}}{{\rm{0}}^{\rm{7}}}{\rm{ m/s}}\) in a circular path \({\rm{2}}{\rm{.00 m}}\) in radius? Antiprotons have the same mass as protons but the opposite (negative) charge. (b) Is this field strength obtainable with today’s technology or is it a futuristic possibility?
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