A rectangular wire loop of width a and height b is connected to a current source

Question

A rectangular wire loop of width a and height b is connected to a current source that, when turned on, gives rise to a current I in the wire. The loop is suspended in a uniform magnetic field that points in a vertical direction (Fig. 28-44), and it would hang vertically if there were no current. We assume that the wire is massless, but two masses m are suspended at the lower comers. What is the angle theta at which the loop is in equilibrium? Calculate this in two ways: by using torques, and by expressing the potential energy as a function of theta and minimizing it. What happens if the direction of the current is reversed?

Explanation / Answer

the torque that the magnetic field exerted to the loop is. T=B*(I*ab)*sin alpha=B*(I*ab)*cos 0 where alpha is the angle between the loop and the horizontal. torque of the gravitation force. 2m*b*sin0. so that we have. 2m*b*sin0=B*I*ab*cos0. so tan0=B*I*a/2m so 0 =arctan (BIa/2m). -------------- energy. potential energy. of the loop inside that magnetic field. E=-Bpsin0. so we have -BIab*sin0-mg*cos0*b=E minimum, take the first derivative. -B*I*a*cos0+mg*sin0=0. so tan0=BIa/2m

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