100 mm The picture shows a device for measuring an object\'s mass. The object ha

Question

100 mm The picture shows a device for measuring an object's mass. The object hangs from a by a string from a horizontal rod. The rod has a current, I, through it directed from left to right. The rod is free to slide up and down the vertical columns with negligible friction, while the rod's orientation remains fixed. The entire unit is placed in an external magnetic field, B, which is perpendicular to the page. The current in the rod is adjusted until the rod and the object are motionless. Once this equilibrium state has been reached, the object's mass can be calculated a. b. c. Draw a freebody diagram of the forces acting on the object/rod combination. What direction should B point in order for the scale to work? How much current is needed to balance the rod if the combined mass of the object and the rod is 0.157 kg and the magnetic field magnitude is 0.150 T?

Explanation / Answer

(a)FBD attached

(b)We need to have magnetic force acting down in order to measure the mass, the current is flowing in +X so the B field according to right hand rule the magnetic field should point Out of page.

If the force acts upwards, then its Into the page.

(c)the magnetic force and the weight balances

I L B = m g

I = m g/L B

I = 0.157 x 9.81/(0.1 x 0.150) = 102.68 A (L = 100 mm = 0.1 m)

Hence, I = 102.68 A

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