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a surveyor is using a magnetic compass 7.0 m below a power line in which there is a steady current of 110 a.
(a) what is the magnetic field in microteslas at the site of the compass due to the power line? (b) will this field interfere seriously with the compass reading? the horizontal component of earths magnetic field at the site is 20 μt.
(a) number
units
(b)
will affect

Explanation:

Step1: Recall magnetic - field formula

The magnetic - field due to a long straight wire at a distance $r$ from it is given by $B=\frac{\mu_0I}{2\pi r}$, where $\mu_0 = 4\pi\times10^{- 7}\ T\cdot m/A$, $I$ is the current in the wire, and $r$ is the distance from the wire.

Step2: Substitute given values

We are given $I = 110\ A$ and $r=7.0\ m$. Substituting into the formula $B=\frac{\mu_0I}{2\pi r}$, we have $B=\frac{4\pi\times10^{-7}\ T\cdot m/A\times110\ A}{2\pi\times7.0\ m}$.
Simplify the expression:
\[

$$\begin{align*} B&=\frac{4\pi\times10^{-7}\times110}{2\pi\times7.0}\ T\\ &=\frac{2\times10^{-7}\times110}{7.0}\ T\\ &=\frac{220\times10^{-7}}{7.0}\ T\\ &\approx3.14\times10^{-5}\ T = 31.4\ \mu T \end{align*}$$

\]

Step3: Compare with Earth's magnetic - field

The horizontal component of Earth's magnetic field at the site is $B_E = 20\ \mu T$. Since $B = 31.4\ \mu T$ and $B>B_E$, this field will interfere seriously with the compass reading.

Answer:

(a) $31.4\ \mu T$
(b) Yes