Example: Magnetic Field

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Problem

A Metal Rod with length 1.2 m and mass 500 g is suspended in a magnetic field of 0.9 T. Determine the current needed suspend the rod without supports.

Figure will be shown here


Solution

Ampere's Force Law

F=cIdl×B

For our problem we have B=0.9T

And we know the necessary Force to hold up the bar without the supports would be equal to the weight of the bar multiplied by the gravitational force.

Fneeded=mass×gravity

F=500*9.81(g*m/s2)

F=4.905(N)

Substituting into Ampere's Law we are left with

4.905=cIdl×0.9(T/N)

Integrating from l=0 to l=1.2 m gives us

4.905=I*1.2*0.9(T*m/N)I=4.905/(1.2*0.9)=4.5417A

In conclusion we would need 4.54 Amps of current to suspend the bar in the magnetic field.