# 2 - Electric Potential and Potential Energy Electric...

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1 Electric Potential Electric Potential • Chapter 17 ( Chapter 17 ( Giancoli Giancoli ) • All sections except 17.6 (electric All sections except 17.6 (electric dipoles) dipoles) Electric Potential and Potential Energy Work-energy theorem: Change in potential energy = work done Gravitational Potential Energy It requires a certain amount of work to raise an object of mass m from the ground to some distance above the ground. i.e. We have increased the potential energy of the object. PE=W= Force x Displacement m m Lower PE Higher PE Electric Potential Energy Find the work done in bringing a charge q from infinitely far away to a distance R from charge Q. + + r R F Q q Charge is moved towards R by increments of r For a small displacement r, the work done is: W = force x displacement = -F r (we have a negative sign as the direction of the force is opposite to the direction of the displacement) r r kqQ r F W 2 = = = = R 2 R r r kqQ - W PE R kqQ PE = *Note: PE 0 when R This is the PE of a charge q when it is a distance R from Q. R r 1 kqQ = PE is a scalar quantity The sign of the charges must be kept in all calculations Depending on the signs of Q and q, the PE could be positive or negative If the PE is positive (when the charges are both positive or both negative), then work must be done on the charge q to bring it closer to Q, increasing its PE. Displacement F q If the PE is negative (when the charges have opposite signs), then the work is done by the charge, decreasing its PE. q + Displacement F © Z. Altounian

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2 Electric Potential Definition : Define the electric potential, V, at a point by the PE of a charge at that point divided by the value of the charge. q PE V = Units for V: J/C The potential, similar to PE, is a scalar quantity. i.e. We must keep the sign of the charges in all calculations For a point charge, Q´ r Q k V q 1 r Q kq V = = This is the potential a distance r from the charge Q´. * This property of the charge Q´ is more fundamental than PE. If we know the potential at a point in space, when we place a charge Q at that point, its PE can be directly give by: PE = QV The potential V at a point can be due to the presence of a single charge or due to many charges. For many charges, Q 1 , Q 2 , Q 3 , . .. , the potential at a point P is given by the superposition principle: + + + = + + + = 3 3 2 2 1 1 3 2 1 p r kQ r kQ r kQ V V V V * Remember to include the sign of the charges Q 1 , Q 2 , Q 3 , . .. , when calculating V p . * If a charge Q is placed at point P its potential energy will be: PE = Q V p P r 1 r 2 r 3 Q 1 Q 2 Q 3 Example : a) Calculate the potential at point P in the figure; Q 1 = 3 μC Q 2 = –6 μC P r 1 =6 cm r 2 =8 cm + V P = V 1 + V 2 m C C m N m C C m N ) 08 . 0 ( ) 10 6 )( / 10 9 ( ) 06 . 0 ( ) 10 3 )( / 10 9 ( 6 2 2 9 6 2 2 9 × × + × × = C J / 10 25 . 2 5 × = 2 2 1 1 r kQ r kQ + = r 1 =6 cm b) What is the potential energy of a charge Q 3 =2 μC when placed at P?
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## This note was uploaded on 04/07/2008 for the course PHI 102 taught by Professor Altonian during the Spring '08 term at McGill.

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2 - Electric Potential and Potential Energy Electric...

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