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Unformatted text preview: R. Kass P132 Sp04 1 Chapter 25: Electric Potential As mentioned several times during the quarter Newtons law of gravity and Coulombs law are identical in their mathematical form. So, most things that are true for gravity are also true for electrostatics! Here we want to study the concepts of work and potential as they apply to the electric field. In the study of mechanics we talk about work done by (or on) the gravitational field. Example: The work (W) done by gravity when a 1 kg mass (m) falls a distance (d) of 1 meter is: W=mgd=(1kg)(9.8m/s 2 )(1m)=9.8 Joules e also talk about the potential energy of an object. Example: A 1kg mass sitting 1m above the earths surface has a potential energy (U) of: U=mgd=(1kg)(9.8m/s 2 )(1m)=9.8 Joules The relationship between work done by gravity on an object and its change in potential energy is: W done by gravity = - U= -(U final-U inital ) hen our 1 kg object falls 1m its potential energy decreases: U= U final-U inital = 0 9.8J =-9.8J The work done by the earths gravitational field is: W done by gravity = - U= -(-9.8J)= +9.8J Fd cos d F Work : force Constant = = = = Fdx cos x d F Work : general In Remember: When an object falls due to gravity its potential energy decreases. Imagine instead of gravity the force on the object was electrostatic. Example: A positive charge (q) of 1 C is in an electric field (E) of 9.8N/C that points down. How much work is done by the E-field if the charge moves 1 m in the direction of E? W E-field =qEd=(1C)(9.8N/C)(1m)=9.8Joules How much does the charges potential energy change when it moves 1m in the direction of E? U= -W done by E-field =-(9.8J)= -9.8J +q E R. Kass P132 Sp04 2 The Electric Potential Defined It turns out to be very useful to define a quantity called the electric potential (V) . The electric field can be calculated from the electric potential and visa versa. The electric potential is just the electric potential energy per unit charge: q U V = electric potential Actually, it is the electric potential difference we want since in analogy with potential energy it is only the change in potential energy that counts: example: In our previous example we said that a 1 kg mass held 1 m above the earths surface had a potential energy of 9.8 J. In doing this problem we (implicitly) assumed that the potential energy at the earths surface was 0J. More correctly, we should say the potential energy difference of a 1 kg mass 1m above the earths surface is 9.8J. q U q U U V V V i f i f = = = electric potential difference The electric potential difference is a scalar quantity. This is one of its virtues. It allows us to calculate the electric field, a vector, from a scalar!...
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