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### College Physics (Urone)

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

# 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 $${\rm{2}}{\rm{.40 \times 1}}{{\rm{0}}^{\rm{6}}}{\rm{\;m/s}}$$.
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 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.

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