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### College Physics (Urone)

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

# A surveyor $${\rm{100 m}}$$ from a long straight $${\rm{200}}\;{\rm{kV}}$$ DC power line suspects that its magnetic field may equal that of the Earth and affect compass readings. (a) Calculate the current in the wire needed to create a $${\rm{5}}{\rm{.00 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{ T}}$$ field at this distance. (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?

1. The current in the wire is obtained as: $${\rm{25 kA}}$$.
2. The current found in the part (a) is very large.
3. The $${\rm{100 m}}$$distance is unreasonably too long for the measurement of magnetic field.
See the step by step solution

## Step 1: Given Data

• voltage in power line is $${\rm{200 kV}}$$
• magnetic field is $$5.00 \times {10^{ - 5}}\;{\rm{T}}$$
• distance from power line is $$100\;{\rm{m}}$$

## Step 2: Define Magnetism

A vector field that can interact with the moving charges and other magnetic substances is known as a magnetic field. Force produced between two objects due to magnetic interactions can be both attractive and repulsive.

## Step 3: Evaluating the current in the wire

(a)

The current is expressed in the terms of magnetic field by the relation: $$I = \frac{{2\pi rB}}{{{\mu _0}}}$$.

Here, the value of $${{\rm{\mu }}_{\rm{0}}}$$ is said to be the permeability of the free space.

\begin{aligned}{}I &= \frac{{2\pi rB}}{{{\mu _0}}}\\ &= \frac{{2\pi \times 100 {\rm{m}} \times \left( {5.00 \times {{10}^{ - 5}}} \right) {\rm{T}}}}{{\left( {4\pi \times {{10}^{ - 7}}} \right) {\rm{T}} \cdot {\rm{m/A}}}}\\ &= 2.5 \times {10^4}\;{\rm{A}}\\ &= 25\;{\rm{kA}}\end{aligned}

Therefore, current in the wire is: $${\rm{25 kA}}$$.

## Step 4: Explaining what is unreasonable

(b)

The current evaluated in the part (a) is very large. The power is too high for standard transmission lines.

## Step 5: Explaining which assumption or premise is responsible

(c) The $${\rm{100 m}}$$ distance is said to be unreasonably long for the measurement of magnetic field. Also parallel cables are used as transmission line, so that there is no net magnetic field produced, for DC power lines.