Recall that torque is defined as τ = r F sin θ, τ = r F sin θ, where F is the applied force, r is the distance from the pivot to where the force is applied, and θ is the angle between r and F. To find the magnitude of the torque as the wire loop spins, consider Figure 20.24, which shows a view of the wire loop from above. The total torque on the shaft is thus twice the toque on one of the vertical segments of the loop. Repeating this analysis on the right vertical segment of the loop shows that the force on this segment is in the direction opposite that of the force on the left segment, thereby producing an equal torque on the shaft. This force produces a torque on the shaft. Again using the right-hand rule, we find that the force exerted on this segment is perpendicular to the magnetic field, as shown in Figure 20.23. Repeating this analysis for the bottom segment-neglect the small gap where the lead wires go out-shows that the force on the bottom segment is upward, again producing no torque on the shaft.Ĭonsider now the left vertical segment of the loop. Thus, the force on the top segment is downward, which produces no torque on the shaft. Curl your right fingers from the current vector to the magnetic field vector and your right thumb points down. The current goes from left to right into the page, and the magnetic field goes from left to right in the plane of the page.
To determine the direction of the force, we use the right-hand rule. First, consider the force on the top segment of the loop. We take the magnetic field to be uniform over the rectangular loop, which has width w and height ℓ, ℓ, as shown in the figure. Let us examine the force on each segment of the loop in Figure 20.23 to find the torques produced about the axis of the vertical shaft-this will lead to a useful equation for the torque on the loop. When current is passed through the wire loop, torque is exerted on it, making it turn the shaft. A vertical loop of wire in a horizontal magnetic field is attached to a vertical shaft.
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