What force is exerted on the water in an MHD drive utilizing a 25.0-cm-diameter tube, if 100-A current is passed across the tube that is perpendicular to a 2.00-T magnetic field? (The relatively small size of this force indicates the need for very large currents and magnetic fields to make practical MHD drives.)
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Final Answer

50.0 N50.0\textrm{ N}

Solution video

OpenStax College Physics, Chapter 22, Problem 36 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. In this question, we consider a magneto-hydro dynamic drive that might be used to power a submarine for example, the advantage being that it's perfectly silent; there's no moving parts in it, well, almost silent I mean... the turbulent water might make some noise but certainly there's no propeller noise and other mechanical parts moving. So we imagine that the diameter of this tube is 25.0 centimeters, and the current going through it is gonna be 100 amps since it's salt water, it can conduct and so there can be a current passing through the water and the magnetic field strength due to these superconducting coils will be 2.00 tesla and we assume that the magnetic field pointing upwards and the electric current pointing to the side or perpendicular and the question is what is direction of force on the seawater? So the force is gonna be the current through the water multiplied by the length of this water, which is the diameter of the tube, and then multiplied by the magnetic field strength times sin of the angle between magnetic field and the current direction. So this is 100 amps times 25.0 times 10 to the minus 2 meters times 2.00 tesla times sin of 90, which is 1, and this is 50.0 newtons. This force is pretty small for pushing an entire submarine and this is the reason why magneto-hydro dynamic drives are not used in practice yet and you know... it's a little bit doubtful that they really could be because this is already a massively high current and a super high magnetic field producing a very small force but you never know... research continues!