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| 184_notes:examples:week12_force_loop_magnetic_field [2018/07/19 13:31] – curdemma | 184_notes:examples:week12_force_loop_magnetic_field [2018/07/19 13:33] – curdemma | ||
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| * We represent the situation with the diagram below. We arbitrarily choose a counterclockwise direction for the current, and convenient coordinates axes. | * We represent the situation with the diagram below. We arbitrarily choose a counterclockwise direction for the current, and convenient coordinates axes. | ||
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| ====Solution==== | ====Solution==== | ||
| In order to break down our approach into manageable chunks, we split up the loop into its four sides, and proceed. It is easy to find the magnitude of the force on each side, since $\theta$ for each side is just the angle between the magnetic field and the directed current. | In order to break down our approach into manageable chunks, we split up the loop into its four sides, and proceed. It is easy to find the magnitude of the force on each side, since $\theta$ for each side is just the angle between the magnetic field and the directed current. | ||
| - | {{ 184_notes: | + | [{{ 184_notes: |
| This gives the following magnitudes: | This gives the following magnitudes: | ||
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| Since these forces point in opposite directions, this means that the net force on the loop is $0$, the loop's center of mass won't move! However, if there was an axis in the middle of the loop, the opposing forces on the opposite sides of the loop would cause the loop to spin. So there could be a [[183_notes: | Since these forces point in opposite directions, this means that the net force on the loop is $0$, the loop's center of mass won't move! However, if there was an axis in the middle of the loop, the opposing forces on the opposite sides of the loop would cause the loop to spin. So there could be a [[183_notes: | ||
| - | {{ 184_notes: | + | [{{ 184_notes: |
| We could also calculate the torque on the loop, using the definition of torque $\vec{\tau} = \vec{r} \times \vec{F}$, where $\tau$ is the torque on the object, $r$ is the distance from the loop to the axis of rotation, and $F$ is the force. | We could also calculate the torque on the loop, using the definition of torque $\vec{\tau} = \vec{r} \times \vec{F}$, where $\tau$ is the torque on the object, $r$ is the distance from the loop to the axis of rotation, and $F$ is the force. | ||