184_notes:examples:week12_force_loop_magnetic_field

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184_notes:examples:week12_force_loop_magnetic_field [2018/07/19 13:33] curdemma184_notes:examples:week12_force_loop_magnetic_field [2021/07/13 12:33] (current) – [Solution] schram45
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 ===Approximations & Assumptions=== ===Approximations & Assumptions===
-  * The current is in a steady state. +  * The current is in a steady state: This means the current in our loop is not changing with time or space, and is just a constant
-  * The magnetic field does not change. +  * The magnetic field does not change: This removes any time or space dependency on our magnetic field. Assuming it constant in magnitude and direction across each segment of wire. Depending on what is producing this magnetic field, this could change the accuracy of this assumption
-  * There are no outside forces to consider.+  * There are no outside forces to consider: We are not told anything about the mass of the wire or anything else that could produce a force on the loop. To simplify our model we will assume there are no outside forces like gravity, or other external magnetic fields acting on our loop. 
 +  * The current in the loop goes counterclockwise: Since this was not specified in the problem we must assume a direction in order to understand the relationship between the magnetic field and current in our wire. This is important for finding the force, which is really a cross product.
  
 ===Representations=== ===Representations===
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 $$\vec{\tau} = IBL^2 \hat{y}$$ $$\vec{\tau} = IBL^2 \hat{y}$$
 This sort of rotating loop is the basis for an electrical motor. Essentially you are transferring electric energy (by providing a current through the loop) to kinetic energy (by making the loop spin). This sort of rotating loop is the basis for an electrical motor. Essentially you are transferring electric energy (by providing a current through the loop) to kinetic energy (by making the loop spin).
 +
 +We can check the direction of our torques by using RHR as this is also a cross product. If we put our fingers in the direction of our separation vectors and curl towards the forces, we will find that the torques are in the same direction which would cause our loop to rotate. Another way we can evaluate our solution is by looking at our forces. By now we should be very comfortable with cross products, so we should expect there to be no force on the top or bottom wire by inspection of the problem. Also, since the magnetic field is constant, both sides of the loop have the same length and the currents flow in opposite directions, we should expect the forces to be in opposite directions as well. These evaluations all line up with our solution.
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