Question

How far from the starter cable of a car, carrying 150 A, must you be to experience a field less than the Earth’s$\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}}\mathbf{T}$ ? Assume a long straight wire carries the current. (In practice, the body of your car shields the dashboard compass.)

Short answer

Therefore, you must be a distance higher 0.600m .

Step-by-step solution

Definition of magnetic field

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.

Given information and formula to use

The Earth’s Magnetic field is,B=$5.00\times {10}^{-5}\mathrm{T}$

Current in the wire is,I=150A

Magnetic field due to current carrying wire at a distance r:

$B=\frac{{\mu }_{o}I}{2\tau \tau r}$………………..(1)

Where ${\mu }_0$is the magnetic permeability of free space.

Step 3: The required distance

Rearranging the equation (1) and substituting the given data we will get

$$\begin{gathered} B=\frac{{\mu }_{0}I}{2\mathrm{\pi r}} \\ r=\frac{4\mathrm{\pi }\times {10}^{-7}\mathrm{N}/{\mathrm{A}}^2\times 150\mathrm{A}}{2\mathrm{\pi }\times 5.00\times {10}^{-5}\mathrm{T}} \\ r=0.60m \end{gathered}$$

Therefore, you must be a distance higher 0.600m .