An airplane with a wingspan of 79.0 m flies parallel to the Earth's surface at a point where the downward component of the Earth's magnetic field is 0.490 × l0−⁴ T.If the induced potential between wingtips is 0.875 V,what is the plane's speed? A)54.3 m/s B)33.9 m/s C)226 m/s D)17 900 m/s E)111 m/s

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Quizplus · Accepted Answer

The induced potential (voltage) $V$ in a conductor moving through a magnetic field is given by the equation $V = Blv$, where $B$ is the magnetic field strength, $l$ is the length of the conductor (in this case, the wingspan of the airplane), and $v$ is the velocity of the conductor (the speed of the airplane). Rearranging this formula to solve for $v$, we get $v = \frac{V}{Bl}$.Given:- $B = 0.490 \times 10^{-4} \, \text{T}$ (the downward component of the Earth's magnetic field)- $l = 79.0 \, \text{m}$ (the wingspan of the airplane)- $V = 0.875 \, \text{V}$ (the induced potential between wingtips)Substituting these values into the formula gives:$$v = \frac{0.875}{(0.490 \times 10^{-4}) \times 79.0} \approx 226 \, \text{m/s}$$Therefore, the plane's speed is approximately 226 m/s.

An Airplane with a Wingspan of 79