# lecture08 - 9/14/11 Physics for Scientists &amp; Engineers...

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9/14/11 Physics for Scientists & Engineers 2, Chapter 23 1

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9/14/11 Physics for Scientists & Engineers 2, Chapter 23 2 An electric ±eld has many similarities to a gravitational ±eld For example, the magnitude of the gravitational force and the electric force are given by Both gravitational and electrostatic forces depend on the inverse square of the distance Both gravitational and electrostatic forces are conservative We can de±ne the electric potential energy in analogy with the gravitational potential energy F g = G m 1 m 2 r 2 F e = k q 1 q 2 r 2
9/14/11 Physics for Scientists & Engineers 2, Chapter 23 3 For a conservative force, the work is path-independent When an electrostatic force acts between two or more charges within a system, we can de±ne an electric potential energy , U , in terms of the work done by the electric ±eld, W e , when the system changes its con±guration from some initial con±guration to some ±nal con±guration e change in the electric potential energy is the negative of the work done by the electric ±eld Δ U = U f U i = W e U i is the initial electric potential energy U f is the final electric potential energy

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9/14/11 Physics for Scientists & Engineers 2, Chapter 23 4 Like gravitational or mechanical potential energy, we must de±ne a reference point from which to de±ne the electric potential energy We de±ne the electric potential energy to be zero when all charges are in±nitely far apart We can then write a simpler de±nition of the electric potential energy taking the initial potential energy to be zero, e negative sign on the work means If E does positive work then U < 0 If E does negative work then U > 0 Δ U = U f 0 = U = W e,
9/14/11 Physics for Scientists & Engineers 2, Chapter 23 5 Let’s look at the electric potential energy when we move a charge in a constant electric ±eld e work done by a constant force is For a constant electric ±eld the force is e work done by the electric ±eld on the charge is W = F d W = q E d = qEd cos θ F = q E

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