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Chapter 4: Q18E (page 948)

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 be5×10-6T , 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=μ0I2πr .

02

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 thanB=0.05BEarth whereBEarth=5×10-5T . The range of distances will be

r=μ0I2πBr=2×10−7×1002.5×10−6r=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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When switch Sin Fig. E25.29 is open, the voltmeter V reads 3.08 V. When the switch is closed, the voltmeter reading drops to 2.97 V, and the ammeter A reads 1.65 A. Find the emf, the internal resistance of the battery, and the circuit resistance R. Assume that the two meters are ideal, so they don’t affect the circuit.

Fig. E25.29.

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