Nonnuclear submarines use batteries for power when submerged.

(a) Find the magnetic field 50.0 cm from a straight wire carrying 1200 A from the batteries to the drive mechanism of a submarine.

(b) What is the field if the wires to and from the drive mechanism are side by side?

(c) Discuss the effects this could have for a compass on the submarine that is not shielded.

A magnetic field is defined as a position in space near a magnet or an electric current where a physical field is formed by a moving electric charge applying force on another moving electric charge.

Distance from the wire, $\mathrm{r}=50.0\mathrm{cm}\left(\frac{1\mathrm{m}}{100\mathrm{cm}}\right)=0.500\mathrm{m}$

Current in the wire,$\mathrm{I}=1200\mathrm{A}$

At a distance of r from the wire, the magnetic field produced by a straight current-carrying conductor can be expressed as,

$\mathrm{B}=\frac{{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{\pi }}$…………….(1)

Where ${\mu }_0$is the magnetic permeability in the vacuum.

(a)

Consider the given values and use equation (1), which will give

$$\begin{gathered} \mathrm{B}=\frac{\left(4\mathrm{\pi }\times {10}^{-7}\mathrm{N}/{\mathrm{A}}^2\right)\times 1200\mathrm{A}}{2\mathrm{\pi }\times 0.50\mathrm{m}} \\ =4.8\times {10}^{-4}\mathrm{T} \end{gathered}$$

Therefore, the magnetic field is$4.8\times {10}^{-4}\mathrm{T}$.

(b)

The net current would be zero because the wires are to and from the driving mechanism and are parallel, resulting in no magnetic field.

Hence, the magnetic field if the wire's drive mechanism is side by side is zero.

(c)

If the wires are not sided by side, the magnetic field generated by the compass will affect it, allowing the compass to provide an incorrect reading. When the wires are placed side by side, the field is zero, so the unshielded compass is unaffected and gives accurate readings.

Therefore, if the wires are side by side, then there would be no effect on the compass.