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Problem 27 Hard Difficulty

An automobile has a vertical radio antenna 1.20 m long. The automobile travels at 65.0 $\mathrm{km} / \mathrm{h}$ on a horizontal road where Earth's magnetic field is 50.0$\mu \mathrm{T}$ , directed toward the north and downward at an angle of $65.0^{\circ}$ below the horizontal. ( a ) Specify the direction the automobile should move so as to generate the maximum motional emf in the antenna, with the top of the antenna positive relative to the bottom. (b) Calculate the magnitude of this induced emf.

Answer

a. \text { eastward }
b. 4.58 \times 10^{-4} V

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Video Transcript

Okay, So, um, here you have. Ah, the north that's pointing into this will be dizzy, hot direction, pointing into the board, Let's say and you have an antenna that's vertically pointing downwards right on. It's connected. And it's tight in this truck that's moving in whichever direction. Um And so, um, this is north. This is the antenna. What you want air for part A. In order to maximize the emotional E. M s in the antenna, you want the antenna to America to be perpendicular to the north direction, um, and North on. And so, in order to do that, we need you. You need 90 degrees here on. And the only way for that to happen is if the eyes, if the truck is moving this way instead of that way or you know this way or this way or whatever else where it's moving to the Yuste, as is given by, uh, this figure as it's given by this set up here. So yes. So, for part, a answer is move truck to the east part B. We have ah EMF induced equals three times all times. V. You know l and V of those are pretty straightforward. Be, however, is not just the 50 micro test, Like your minutes, the component of 50 perpendicular to emotion. So, um, this is if this you consider if this could be if this is north, uh, that's where the magnetic field is directed. It's directed 65 degrees below, um, and, um right. And so, uh, motion is perpendicular to the magnetic field. And so, uh, this will be so this right here component this year component is the B component in the UAE direction of ze direction. Whatever have you? But it will be s o. This will be be co sign data and data. Um, data is looks terrible. Be co sign data data is just a single. So the induced your mouth will be be coast data. L do. So be is 50 micro Tesla 50 times 10 to the negative six uh, co sign of 65 degrees that times length, which is, uh, times length is 1.2 meters and then a pesky velocity Given in units of kilometers per hour, it's about 65 kilometers per hour. So 65,000 meters per hour. So you multiply by one over 3600. That's the number of seconds in an hour. Get rid of the hour. You get answered meters per second. Um, now you get something and leaders for second. And the final units are in vaults, and the answer is 4.6 times 10 to the negative four volts or close to 40.5. Milly, uh, volts.

New Mexico State University
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