A straight 2.00-m, 150-g wire carries a current in a region where the earth\'s m

Question

A straight 2.00-m, 150-g wire carries a current in a region where the earth's magnetic field is horizontal with a magnitude of 0.55 gauss. a) What is the minimum value of the current in this wire so that its weight is completely supported by the magnetic force due to earth's field, assuming that so other forces except gravity act on it?  Does it seem likely that such a wire could support this size of current ? b) Show how the wire would have to be oriented relative to the earth 's magnetic field to be supported in this way?

Explanation / Answer

a). Magnetic force exerted on a wire. F=I*lxB. where l be length vector of the wire and B be the magneticfield. for F=mg (g be the gravity acceleration vector). so I*lxB=mg. so I*l*sin*B=mg. so I=mg/(lsinB) I is minimum when sin=1. so I=mg/(lB)=...... --------- b). Let assume that the magnetic force is horizontal and go fromleft to right in front of our face. Using left hand rule. (or you can use the vector equationabove---IlxB=gm). Then the current go directly into our face. and also horizontal(perpendicular to the field).

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