Chapter%2018_Electric%20Potential%20and%20Capacitance - 1 18.1 Electric Potential Energy The electric force like the gravitational force is a

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2 18.1 Electric Potential Energy The electric force, like the gravitational force, is a conservative force. ( Conservative force: The work is path-independent. ) As in mechanics, work is Work done on the positive charge by moving it from A to B A B E !" d q cos Fd W = qEd Fd W = = q cos
3 The work done by a conservative force equals the negative of the change in potential energy, D PE This equation is valid only for the case of a uniform electric field PE W qEd D = - = If a charged particle moves perpendicular to electric field lines, no work is done. if d ^ E
4 The potential difference between points A and B, V B -V A , is defined as the change in potential energy (final minus initial value) of a charge, q, moved from A to B, divided by the charge Electric potential is a scalar quantity Electric potential difference is a measure of electric energy per unit charge Potential is often referred to as “voltage” B A PE V V V q D D = - = If the work done by the electric field is zero, then the electric potential must be constant
5 Electric potential difference is the work done to move a charge from a point A to a point B divided by the magnitude of the charge. Thus the SI units of electric potential difference In other words, 1 J of work is required to move a 1 C of charge between two points that are at potential difference of 1 V Question: How can a bird stand on a high voltage line without getting zapped? 1 1 V J C =
6 Units of electric field (N/C) can be expressed in terms of the units of potential (as volts per meter) Because the positive tends to move in the direction of the electric field, work must be done on the charge to move it in the direction, opposite the field. Thus, A positive charge gains electric potential energy when it is moved in a direction opposite the electric field A negative charge looses electrical potential energy when it moves in the direction opposite the electric field 1 1 N C V m =
7 Analogy between electric and gravitational fields The same kinetic-potential energy theorem works here If a positive charge is released from A, it accelerates in the direction of electric field, i.e. gains kinetic energy If a negative charge is released from A, it accelerates in the direction opposite the electric field A B q d A B m d E !" g !" i i f f KE PE KE PE + = +
8 Example: motion of an electron V ab What is the speed of an electron accelerated from rest across a potential difference of 100V? Given: D V=100 V m e = 9.11 × 10 -31 kg m p = 1.67 × 10 -27 kg |e| = 1.60 × 10 -19 C Find: v e =? v p =? s m v s m v m V q v V q mv V q PE KE KE PE KE PE KE p e f f i f f f i i / 10 3 . 1 / 10 9 . 5 2 2 1 5 6 2 ´ = ´ = D - = D - = D - = D = - + = +
9 18.2 Electric potential and potential energy due to point charges Electric circuits: point of zero potential is defined by grounding some point in the circuit Electric potential due to a point charge at a point in space: point of zero potential is taken at an infinite distance from the charge With this choice, a potential can be found as

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