Question

Certain bacteria (such as Aqua spirillum magnetotacticum) tend to swim toward the earth’s geographic north pole because they contain tiny particles, called magnetosomes, that are sensitive to a magnetic field. If a transmission line carrying 100 A is laid underwater, at what range of distances would the magnetic field from this line be great enough to interfere with the migration of these bacteria? (Assume that a field less than of the earth’s field would have little effect on the bacteria. Take the earth’s field to be$\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}}\mathit{T}$ , and ignore the effects of the seawater.)

Short answer

If the bacteria are within r = 8m of the cable, its magnetic field may be strong enough to affect their sailing.

Step-by-step solution

The formula of the magnetic field

For a very long wire, the magnetic field is given by$\mathit{B}\mathbf{=}\frac{{\mathbf{\mu }}_{\mathbf{0}}\mathbf{I}}{\mathbf{2}\mathbf{\pi r}}$ .

Use the formula to calculate the range of distance

Given that a field less than 5% of the earth’s field would have little effect. So, the minimum field produced by the transmission line must be larger than$B=0.05B_{Earth}$ where$B_{Earth}=5\times {10}^{-5}T$ . The range of distances will be

$\begin{array}{r}r=\frac{{\mu }_{0}I}{2\pi B}\\ r=\frac{2\times {10}^{-7}\times 100}{2.5\times {10}^{-6}}\\ r=8m\end{array}$

So, if the bacteria are within r = 8 m of the cable, its magnetic field may be strong enough to affect their sailing.