The drawing shows a thin, uniform rod, which has a length of 0.59 m and a mass o

Question

The drawing shows a thin, uniform rod, which has a length of 0.59 m and a mass of 0.123 kg. This rod is attached to the floor by a hinge at point P. A uniform magnetic field of 0.40 T is directed perpendicular to the rod, as shown. There is a current I = 3.6 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.)

The drawing shows a thin, uniform rod, which has a length of 0.59 m and a mass of 0.123 kg. This rod is attached to the floor by a hinge at point P. A uniform magnetic field of 0.40 T is directed perpendicular to the rod, as shown. There is a current I = 3.6 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

equilibrium=>P=0
=>B*I*L(L/2)=mg*(L/2)cos?
B=0.4
I=3.6
L=0.59
m=0.123
=>cos?=B*I*L/mg
           =0.4*3.6*0.59/0.123*9.8
           =0.7048
=>?=45.18 degrees

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