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Electric

Electric. Potential. and. Energy. Gravity Redux. Imagine moving a mass through a height somewhere near the earth’s surface. H. How much work did this require? W= D E = D PE=mgH The amount of work depends on the mass.

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Electric

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  1. Electric Potential and Energy

  2. Gravity Redux Imagine moving a mass through a height somewhere near the earth’s surface. H How much work did this require? W=DE = DPE=mgH The amount of work depends on the mass. Is there a property associated with this energy change that does not depend on the weight moved?

  3. Now imagine moving a charge in a region of electric field created by a charge distribution: This, too, takes work. There is a field created by the other charges, and moving our charge requires that we overcome the force exerted through this field. The work is directly related to the amount of charge moved. Can we define a quantity related to this energy change that does not depend on the charge moved?

  4. Electric Potential Difference ∆V is called the “electric potential difference” between the two points. Its units are: The potential difference between two points is determined by the charges that create the electric field, but it does not depend on any charge that might be moved between the two points. Note the similarity with the gravitational analogy where ∆y did not depend on the mass moved. Example: It takes 3.2 J to move a 400µC charge between two points separated by 8 m. Find the potential difference between the two points. Note: There is no dependence on the 8 m, the distance between the points

  5. Example: Find the work needed to move a 2 µC between the two points of the previous problem. ∆V is the same so: When a charge is moved (slowly) as in our definition for potential difference, the agent moving the charge is repositioning it. Thus, there has been a change in potential energy. Therefore,

  6. As +ive charge moves to lower potential, it loses PE and gains KE As mass moves to lower height, it loses PE and gains KE

  7. Example: A proton initially moving at 3x105 m/s moves through a potential difference of 200V traveling in the same direction as the electric field. The field does work on the proton by accelerating it. What is its new velocity? When an electron or proton moves through a 1 V potential difference, the change in energy is defined to be 1 electron-volt, 1eV. How many joules is this?

  8. Equations involving electric potential Consider moving a test charge against a uniform electric field: d refers to the displacement along the field lines.

  9. Equipotential surfaces Suppose we have a uniform e-field, and we move a test charge perpendicular to the field. How much work does this take? none, since the potential difference between the two points is zero! A connected surface along which no work is required to move a charge is called an equipotential surface. Note that electric field lines will always be perpendicular to the surface.

  10. What happens when a conductor is placed in an electric field? _ _ _ _ _ + + + + + Within the conductor, the field quickly vanishes as polarization occurs. At the surface, field lines must come in at right angles, otherwise charges on the surface will scoot along the surface, contrary to the observed equilibrium. Thus, the conductor becomes an equipotential surface.

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