A thin uniform conducting ro has a length of 0.50 meters and a mass 0.100 kg. It

Question

A thin uniform conducting ro has a length of 0.50 meters and a mass 0.100 kg. It is attached to the floor by a hinge. A uniform magnetic field of 0.45 T is parallel to the floor and points perpendicularly to the rod as shown (into the page of the diagram). When a current flows upwards through the rod it suspends itself at an angle of 35 degrees above the floor. Use torque balance to determine the magnitude of the current. Choose the axis at the hinge and assume the magnetic force acts at the center of mass of the rod (which is the midpoint) as does the weight. Draw a force diagram showing the correct directions of the two forces acting on the rod which contribute to the torque (the force at the hinge itself contributes no torque if the axis is chosen at the hinge) and calculate the lever arm for each force. This will help you set up the torque equation that you need to solve the problem.

Explanation / Answer

Force due to magnetic field on the conducting rod Fm=i(lxB) sin45=i(0.5x0.45)x0.7=0.16i where i is the current, B is the magnetic field and l is the length of the rod. This force acts through the centre of mass of the rod and it produces a torque which counterbalances the torque due to the weight of the rod also acting through its centre of mass.

The torque t1 due to the field is t1=rx Fm sin35=l/2xBil xsin45xsin35=0.25x0.16x0.6i=0.02i

The torque due to the weight of the rod t2=rxFg= l/2x mg cos 55=0.5/2x0.1x9.8xcos55=0.14

Since t1=t2 wehave

0.02i=0.14

Therefore, i=0.14/0.02=7 amp

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