chapter25

chapter25 - Quiz on the math needed today B What is the...

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Quiz on the math needed today What is the result of this integral: B A dx x 2 1 )? ( is what , ) ( ) ( and known is ) ( If x z dx x z x y x y = )? ( is what , ) ( ) ( and known is ) ( If integral line r z s r z r r = d y y B A x dx x B A B A 1 1 1 1 2 - = - = dx x dy x z ) ( ) ( = k j i r r z ˆ ˆ ˆ y x x x system coordinate Cartesian a In ), ( ) ( + + =
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Chapter 25 Electric Potential
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A review of gravitational potential B When object of mass m is on ground level B, we define that it has zero gravitational potential energy. When we let go of this object, if will stay in place. When this object is moved to elevation A, we say that it has gravitational potential energy mgh . h is the distance from B to A. When we let go of this object, if will fall back to level B. A When this object is at elevation A, it has gravitational potential energy U A -U B = mgh . U A is the potential energy at point A with reference to point B. When the object falls from level A to level B, the potential energy change: Δ U = U B -U A The gravitational force does work and causes the potential energy change: W = mgh = U A -U B = - Δ U h mg We also know that the gravitational force is conservative: the work it does to the object only depends on the two levels A and B, not the path the object moves.
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Introduction of the electric potential, a special case: the electric field is a constant. E F 0 q = When a charge q 0 is placed inside an electric field, it experiences a force from the field: When the charge is released, the field moves it from A to B, doing work: Ed q q 0 0 W = = = d E d F If we define the electric potential energy of the charge at point A U A and B U B , then: U U U Ed q B A - = - = = 0 W If we define U B =0, then U A = q 0 Ed is the electric potential energy the charge has at point A. We can also say that the electric field has an electric potential at point A. When a charge is placed there, the charge acquires an electric potential energy that is the charge times this potential.
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Electric Potential Energy, the general case When a charge is moved from point A to point B in an electric field, the charge’s electric potential energy inside this field is changed from U A to U B : A B U U U - = E F 0 q = The force on the charge is: = = - = - B A B A d q W U U U s E 0 force) field the (of So we have this final formula for electric potential energy and the work the field force does to the charge: When the motion is caused by the electric field force on the charge, the work this force does to the charge cause the change of its electric potential energy, so: U W - =
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discussion Electric force is conservative. The line integral does not depend on the path from A to B; it only depends on the locations of A and B. = -
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chapter25 - Quiz on the math needed today B What is the...

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