Lesson 16 Electric Potential

Transcription

1 Physics 30 Lesson 16 Electric Potential I. Gravitational otential energy revisited There are many similarities between gravitational otential energy and electric otential energy. To hel us understand electric otential energy, it may be helful to review gravitational otential energy and extend the concets we have learned. When a mass is laced in a gravitational field it has a certain amount of otential energy relative to a starting osition. In the diagram to the right: If the mass is moved toward A, there is a gain in gravitational otential energy. If the object is moved toward B, there is a loss of gravitational otential energy. If the object is moved toward C, there is no change in the energy. II. Electric otential energy Refer to Pearson ages 560 to 566. A B Earth C Charged objects in electric fields behave in a similar way to masses laced in gravitational fields. For examle, a small ositive charge (+) is laced in the electric field created by the ositive and negative charges as shown in the diagram below. A + B C If + is moved toward A, work (i.e. W = F d) must be done against the electric field the electric otential energy of the charge increases. If + is moved toward B, work is done by the electric field the electric otential energy of the charge decreases. If + is moved toward C, no work is done since no force is reuired to move it in that direction the electric otential energy of the charge does not change. Electric Potential Energy (E P ) is the energy of a charged object due to its osition in an electric field. Dr. Ron Licht

2 III. Electric otential When we were working with gravitational otential energy, we were interested in changes in gravitational otential a change in the osition of a mass within a gravitational field. In a similar manner, a change in electric otential is due to a change in the osition of a charge within an electric field. The symbol for electric otential is V and its unit is the Volt. In reality, it is not ossible to measure the absolute electric otential at a oint in an electric field, but we can measure the electric otential difference (V) between two oints. Consider the following diagram B A Q A ositively charged article, with a charge of, has a certain amount of electric otential at osition B (V B ) and a different amount of electric otential at osition A (V A ). The difference in otential is given by: V = V B - V A Thus, when a charged article is allowed to move from osition B to osition A the electric field does work on the article and the article s kinetic energy increases. Conversely, if the article is moved from A to B work must be done against the electric field. Electric otential is the change in electric otential energy er unit of charge. V V E Joule Coulomb J C Volt (V) Note: Electric otential (V) is a scalar term. (Direction does not matter.) Examle 1 If 5.0 J of energy is reuired to move a 1.0 C charge in an electric field, then the otential difference between the two oints is? E V 5.0J V 1.0 C V 5.0 V Dr. Ron Licht 16

3 Examle If 1.0 x J of energy is reuired to move a roton in an electric field, what is the otential difference between the starting oint and the finishing oint in the field? E V Examle J V C V 6.5 V The otential difference between two oints is 10 Volts, what is the work reuired to move a 6.0 x 10-4 C against the field? W V 4 W C(10V) - W J Examle 4 An alha article is laced in an electric field with a otential difference of 100 V. If the alha article is released within the field, what is the maximum seed that the alha article could attain? From the formula/data sheet: Rest Mass Charge Alha article... m = 6.65 x 10-7 kg + The + charge is converted to a charge in Coulombs by multilying it by the elementary charge. = + x 1.6 x C = + 3. x C Using the rincile of the conservation of energy, the electric otential energy of the article in the electric field (E = V) is transformed into kinetic energy (E k ). E E V v v k 1 mv V m 19 (3.10 C)(100 V) kg v m s Note: This examle is a very common alication of converting electric otential energy into the kinetic energy of a charged article. We will be using this idea throughout the rest of the course. Dr. Ron Licht

4 IV. Euiotential Lines Quite often, two arallel lates are a simle way to create a otential difference (we will discuss arallel lates in detail in Lesson 17). In such an electric field, one can ma out what the electric otential is at different oints. Along an imaginary line arallel to the lates, the electric otential is the same or eual. The subseuent euiotential lines have the same otential at all oints on the line. electric field euiotential Note: + line line euiotential lines are erendicular x B x A to field lines x C 40 V 35 V 30 V 5 V 0 V 15 V 10 V 5 V 0 V OR +0 V +15 V +10 V +5 V 0 V -5 V -10 V -15 V -0 V The diagram above shows electric field lines and euiotential lines for a arallel late system consisting of a (+) late and a () late. The dotted lines reresent the euiotential lines which are always erendicular to the electric field lines. For this articular examle there is a otential difference of 40 volts between the two lates. Note that what we call our 0 V otential line is uite arbitrary, it is the difference in otential between two oints that really counts. If, for examle, a roton were to move from A to B, work would have to be done and its otential energy would increase. Similarly, since C and A lie on the same euiotential line, moving a roton from C to B would reuire the same amount of work as moving it from A to B. Conversely, if a roton is moved from B to A or B to C, its otential would decrease. Moreover, moving the roton from A to C would not result in any energy change. Examle 5 Using the arallel late system shown above: A. If an alha article is moved from A to B, what energy would be reuired? E V 19 E C(0V) -18 E J B. If a 7.0 C charge is allowed to move from B to A and its mass is.0 mg, what is its final seed if it starts from rest? 6 E E (7.010 C)(0 V) k v 6 1 V mv.010 kg v 11.8 m s V v m Dr. Ron Licht

5 Examle 6 A beryllium ion (Be + ) is accelerated through a MV otential difference. If its final seed is.53 x 10 6 m/s what is its mass? The + charge is converted to a charge in Coulombs by multilying it by the elementary charge. = + x 1.60 x C = x C E E V m m k 1 mv V v 19 6 ( C)( V) m kg 6 ms V. Practice roblems 1. If 50 J of work is reuired to move a 0.50 C charge in an electric field, what is the otential difference between the two oints? (100 V). If an electron starting from rest falls through a otential difference of 500 V, what is its final seed? (1.33 x 10 7 m/s) 3. A comletely ionized aluminium nucleus (i.e. all of the electrons have been stried from the atom) is accelerated through a 0.5 MV otential difference. What is its final seed? (4.8 x 10 6 m/s) Dr. Ron Licht

6 VI. Hand-in assignment J of work is done on a charge of 80 C as it jums across a sark ga in the sark lug of a car. What was the otential difference across the ga? (50 V). What maximum seed will an alha article reach if it moves from rest through a otential difference of 6500 V? (7.9 x 10 5 m/s) 3. How much kinetic energy does a comletely ionized fluorine nucleus have when it is accelerated by a otential difference of 0.60 MV? What is it seed? (Note: The term comletely ionized means that all of the electrons have been stried away from the nucleus of an atom. Therefore, its charge is eual to the number of rotons in the nucleus.) (8.64 x J, 7.4 x 10 6 m/s) 4. An alha article is accelerated to 1/10th the seed of light. What minimum otential difference is reuired to do this? (9.35 MV) 5. Assuming that it started from rest, what is the momentum of a roton after it has gone through a otential difference of 0.0 kv? (3.7 x 10-1 kgm/s) 6. Consider the following diagram of euiotential lines 140 V 10 V 100 V 80 V 60 V 40 V 0 V 160 V 0 V + A D B C E A. What energy is reuired to move an alha article from E to C? B. If an electron were laced at D, what would its maximum seed be at B? C. What is the energy reuired to move a roton from C to A? D. What is the energy reuired to move a neutron from E to A? 7. An electron is released from rest adjacent to the negative late in a arallel late aaratus. A otential difference of 500 V is maintained between the lates, and they are in a vacuum. With what seed does the electron collide with the ositive late? (1.3 x 10 7 m/s) 8. An electron with a velocity of 5.0 x 10 6 m/s is injected into a arallel late aaratus through a hole in the ositive late. It moves across the vacuum between the lates, colliding with the negative late at 1.0 x 10 6 m/s. What is the otential difference between the lates? (68 V) Dr. Ron Licht