You are working on a project to make a more efficient engine. Your team is investigating the possibility of making electrically controlled valves that open and close the intake and exhaust openings for an internal combustion engine. This device is mounted on an axis so that it can spin freely to close the valve. Your assignment is to determine the stability of the valve by calculating the force on each of its sides and the net force on the valve. (Another team-member is calculating the torques on the device and needs your results to do this.) You may neglect any forces other than magnetic forces. For example, neglect forces due to the intake/exhaust when the device is in operation.
You are working on a project to make a more efficient engine. Your team is investigating the possibility of making electrically controlled valves that open and close the intake and exhaust openings for an internal combustion engine. This device is mounted on an axis so that it can spin freely to close the valve. Your assignment is to determine the stability of the valve by calculating the force on each of its sides and the net force on the valve. (Another team-member is calculating the torques on the device and needs your results to do this.) You may neglect any forces other than magnetic forces. For example, neglect forces due to the intake/exhaust when the device is in operation.
The valve is made of a thin but strong rectangular piece of non-magnetic material that has a current-carrying wire along its edges. The rectangle is 0.35 cm x 1.83 cm. The valve is placed in a uniform magnetic field of 0.15 T such that the field lies in the plane of the valve and is parallel to the short sides of the rectangle. The region with the magnetic field is slightly larger than the valve. When a switch is closed, a 1.7 A current enters the short side of the rectangle on one side and leaves on the opposite short side of the rectangle. At the suggestion of a colleague, who is hoping to ensure different currents along the sides of the valve, resistors have been included along the wire on each of the short sides of the valve. The value of the resistor on one side is twice that on the other side.
A diagram of the valve is show below:
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