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Chapter 4: Q18E (page 948)

Certain bacteria (such as Aqua spirillum magnetotacticum) tend to swim toward the earth鈥檚 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鈥檚 field would have little effect on the bacteria. Take the earth鈥檚 field to be5脳10-6T , and ignore the effects of the seawater.)

Short Answer

Expert verified

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

01

The formula of the magnetic field

For a very long wire, the magnetic field is given byB=渭0I2蟺谤 .

02

Use the formula to calculate the range of distance

Given that a field less than 5% of the earth鈥檚 field would have little effect. So, the minimum field produced by the transmission line must be larger thanB=0.05BEarth whereBEarth=5脳10-5T . The range of distances will be

r=渭0I2蟺Br=2脳10鈭�7脳1002.5脳10鈭�6r=8m

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

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