Magnetic Support
What must the current in the conductor be if the magnetic force is to support the weight of the conductor?
A conductor 45 cm long, with a mass of 15g, lies in a horizontal position at a 90º angle to a uniform horizontal magnetic field of magnitude 0.20 T. What must the current in the conductor be if the magnetic force is to support the weight of the conductor?
***10 POINTS FOR BEST ANSWER!!!
Use the equation for the Lorentz force:
F = i*L × B
In the case of perpendicular wire and B-field, the cross product can be treated as normal multiplication.
F = i*L*B
Solve for i:
i = F/(L*B)
The force should be equal to the weight of the wire, which is mass * gravity field:
F = m*g
Substitute:
i = (m*g)/(L*B)
Plug in data:
m:=0.015 kg; B:= 0.2 Teslas; L:=0.45 m; g:= 9.8 N/kg
Result:
i = 1.633 Amperes
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