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# Physics 2 - PROBLEM SET 29.1-3 Are Coulomb Forces...

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PROBLEM SET 29.1-3 “Are Coulomb Forces Conservative?” As you may recall from mechanics, some forces have a very special property, namely, that the work done on an object does not depend on the object's trajectory; rather, it depends only on the initial and the final positions of the object. Such forces are called conservative forces. If only conservative forces act within a closed system, the total amount of mechanical energy is conserved within the system (hence the term "conservative"). Such forces have a number of properties that simplify the solution of many problems. You may also recall that a potential energy function can be defined with respect to a conservative force: This property of conservative forces will be of particular interest of us. Not all forces that we deal with are conservative, of course. For instance, the amount of work done by the frictional force (or any other kind of frictional force) very much depends on the object's trajectory. Friction, therefore, is not a conservative force. On the other hand, the gravitational force and the normal force are examples of conservative forces. What about electrostatic (Coulomb) forces? Are they conservative? Is there a potential energy function associated with an electrostatic field? Let us try to find out. In this problem, you will be asked to use the given diagram to calculate the work done by the electric field r E on a particle of charge q and see for yourself whether that work appears to be trajectory-independent. You will use the formula for Coulomb force r F = q r E and the definition of work. A reminder: The work W done by a constant force can be found as W = r F r d cos θ where r F is the magnitude of the force acting on the object, r d is the magnitude of the displacement that the object undergoes, and θ is the angle between the vectors r F and r d .

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