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Chapter 29: Problem 30

A supersonic aircraft with a wingspan of \(10.0 \mathrm{~m}\) is flying over the north magnetic pole (in a magnetic field of magnitude 0.500 G perpendicular to the ground) at a speed of three times the speed of sound (Mach 3). What is the potential difference between the tips of the wings? Assume that the wings are made of aluminum.

Short Answer

Expert verified
Answer: The potential difference between the tips of the wings is approximately 5.14 mV.

Step by step solution

01

Convert the magnetic field strength from G to Tesla

The given magnetic field strength is 0.500 G. We need to convert it into Tesla (T) before substituting it into the EMF formula. Since 1 G = 10^-4 T, we find: \(B = 0.500\,\mathrm{G} \times 10^{-4}\,\frac{\mathrm{T}}{\mathrm{G}} = 5.0\times 10^{-5}\,\mathrm{T}\)
02

Find the speed of sound in air

Standard speed of sound in air is approximately 343 m/s. Since the aircraft is flying at Mach 3, its actual speed is three times this value: \(v = 3\times 343\,\mathrm{\frac{m}{s}} = 1029\,\mathrm{\frac{m}{s}}\)
03

Calculate the electromotive force (EMF)

Now that we have all values needed, we can calculate the potential difference between the tips of the wings using the formula for EMF: EMF = B * L * v EMF = \((5.0 \times 10^{-5}\,\mathrm{T}) \times (10.0\,\mathrm{m}) \times (1029\,\mathrm{\frac{m}{s}})\) EMF = \(5.1415\times 10^{-3}\,\mathrm{V}\)
04

Round the answer

Finally, let's round the answer to two decimal places: EMF = \(5.14\times 10^{-3}\,\mathrm{V}\) Therefore, the potential difference between the tips of the wings is approximately 5.14 mV.

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