2 - E fields _ dipoles

2 - E fields _ dipoles - Electrostatics Demo of static...

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Electrostatics Demo of static charges
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Coulomb’s Law: Force by q 1 on q 2 1 2 12 2 ˆ e q q k r = F r r 9 2 2 0 1 8.9875 10 N m /C 4 e k !" = = # = unit vector from q 1 to q 2 r r r r = ˆ F 12 = - F 21 Newton’s 3rd Law Equal, opposite and on DIFFERENT bodies. Coulomb's Law
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Meaning of the “unit vector” We want a way to show the direction of the force. Force is a vector, so it has magnitude and direction. F has (magnitude)(direction). Create a vector that shows direction, but does not change magnitude. It has length = 1, a “unit” vector. Notation in Wolfson: general vector has an arrow over it. unit vector has a carat (hat) over it. magnitude has ordinary letter
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Applying Coulomb’s Law Find each F ij separately (vectors) of charges q i acting on charge q j . Add the vector’s components (superpose) Resultant F is the vector sum.
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Electric Field Described A charge does not exert a force on itself. If a small* test charge, q, feels an electric force, F , at a position r we say there exists an electric field E at r. It is just a way to say what the electric effect of all the other charges is. Define E ( r ) = F (on q due to all charges other than q) / q . *Small so it does not disturb the charges that cause the field.
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E of point charge q The force that a test charge q t feels due to the presence of a point charge q, a distance r away, is F = kq q t r /r 2 We seek a quantity E such that when we multiply E by q t we get the force that q t feels. This is E = F / q t = kq r /r 2 q is the source of the field that acts on any other charge that is placed at r .
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Two Ways to Draw E Fields Magnitude illustrated by either Density of lines Lengths of Vectors Here, - charge is the source: “Pusher” + “Pushee” The problem decides whether a charge is acting as a source or as a “pushee”.
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Electric Dipole as a source- on axis As an example of calculating E from multiple charges, derive E along the axis of a dipole P = q d . (Wolfson derives E = - kp/y
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2 - E fields _ dipoles - Electrostatics Demo of static...

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