Lecture 6 - Electrostatic Potential Energy Electrostatic...

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lectrostatic Potential Energy Electrostatic Potential Energy • Reminder: –Wo rk ( r 1 Æ r 2 )= F •d r , evaluated from a starting value r 1 to an ending value r 2 . – For conservative forces, Δ PE( r 1 Æ r 2 ) = -W( r 1 Æ r 2 ). • What’s new: he electric force is conservative – The electric force is conservative. – So the electric potential energy of a charge q is Δ PE ( r Æ r )= - q E •d r . E 1 2 – And the total energy of a charged object experiencing only electric forces satisfies Δ (KE+PE E )=0.
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xample: PE of q field of q Example: PE of q 2 in field of q 1 • We first find the work = = = = = 2 1 2 1 2 2 1 1 1 | ' ' ' ) ' 0 ' ( 1 2 2 q q q q dr q q r r W r r r • The PE is the negative of the work and can be used with onservation of energy Note this result is valid for any 2 1 0 0 0 4 4 4 1 r r r r r πε conservation of energy. Note this result is valid for any “point-charge-like” field. 1 1 q q E E E 2 1 0 2 1 1 2 4 ) ' 0 ' ( r r PE PE r r PE = = = = Δ 1 0 2 1 1 2 0 2 1 2 4 4 r q q KE r q q KE + = +
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xample: a particle expelled from U- 38 Example: a particle expelled from U 238 An α -particle is a 4 He nucleus with 2 protons+2 p p neutrons. 238 U undergoes a decay: 238 U Æ α + 234 Th. • Suppose the a particle has 0 KE at the surface of the 34 234 Th nucleus. What will the speed of the α -particle be when very far away. Take the 234 Th nuclear radius to be R h = 7.7×10 -15 m. Th • We use conservation of energy: KE 1 +PE 1 =KE 2 +PE 2 . •K E 1 =0. PE 1 =k(2e)(90e)/R Th =5.4×10 -12 J. • Very far away, PE 2 =0, so KE 2 =PE 1 =M He v 2 /2. • And v=4.1 m/s.
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E and PE- er- harge PE and PE per charge • It is often useful to adopt the convention PE(r= )=0. p( ) With this, we can define the PE of a pair of point charges as PE=kq 1 q 2 /r. The PE is positive for same-sign charges nd increases as the charges get closer together The and increases as the charges get closer together. The behavior is opposite for opposite-sign charges.
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Lecture 6 - Electrostatic Potential Energy Electrostatic...

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