The drawing shows a thin, uniform rod, which has a length of 0.40 m and a mass o

Question

The drawing shows a thin, uniform rod, which has a length of 0.40 m and a mass of 0.149 kg. This rod is attached to the floor by a hinge at point P. A uniform magnetic field of 0.46 T is directed perpendicular to the rod, as shown. There is a current I = 5.1 A in the rod, which does not rotate clockwise or counterclockwise. Find the angle ?. (Hint: The magnetic force may be taken to act at the center of gravity.)

Number Units TdegV/mC/kgN The drawing shows a thin, uniform rod, which has a length of 0.40 m and a mass of 0.149 kg. This rod is attached to the floor by a hinge at point P. A uniform magnetic field of 0.46 T is directed perpendicular to the rod, as shown. There is a current I = 5.1 A in the rod, which does not rotate clockwise or counterclockwise. Find the angle ?. (Hint: The magnetic force may be taken to act at the center of gravity.)

Explanation / Answer

torque due to gravity equals to torque due to magnetic field (rod doesn't move)

F(gravity)*0.58length*cos(angle)=F(magnetic f)*lenght*0.5

so

mg*0.5length*cos(angle)=I*B*length*0.5*length

after simplification, angle=63 degrees

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