Magnetic levitation A metal rod of length w = 19 cm and mass m = 55 grams has me

Question

Magnetic levitation
A metal rod of length w = 19 cm and mass m = 55 grams has metal loops at both ends, which go around two metal poles (see the figure).

The rod is in good electrical contact with the poles but can slide freely up and down. The metal poles are connected by wires to a battery, and a current I = 9 amperes flows through the rod. A magnet supplies a large uniform magnetic field B in the region of the rod, large enough that you can neglect the magnetic fields due to the 9ampere current. The large magnetic field is oriented to have the maximum effect.

The rod floats at rest h = 9 cm above the table. What is the magnetic field in the region of the rod? Assume +x is to the right, +y is up, and +z is out of the page.

<  ,  ,  > T
Which of the following statements are true?

If the conventional current in the bar were less than 9 A, the bar would fall.The magnetic force on the bar is in the +y direction (upward).If the conventional current in the bar flowed in the opposite direction (to the left), the bar would still float at rest 9 cm above the table.

Explanation / Answer

A)
magnetic force = gravitational force

B*I*L*sin(90) = m*g

B = m*g/(I*L)

= 0.055*9.8/(9*0.19)

= 0.3152 T

direction of B is into the page (-z)

B)

Which of the following statements are true?

If the conventional current in the bar were less than 9 A, the bar would fall. (true)

The magnetic force on the bar is in the +y direction (upward). (true)

If the conventional current in the bar flowed in the opposite direction (to the left), the bar would still float at rest 9 cm above the table. (false)

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