CHAPTER 19 - ELECTRIC POTENTIAL ENERGY AND ELECTRIC POTENTIAL. Sections 1-5

Transcription

1 CHAPTER 19 - ELECTRIC POTENTIAL ENERGY AND ELECTRIC POTENTIAL Sections 1-5

2 Objectives: After completing this unit, you should be able to: Understand an apply the concepts of electric potential energy, electric potential, and electric potential difference. Calculate the work required to move a known charge from one point to another in an electric field created by point charges. Write and apply relationships between the electric field, potential difference, and plate separation for parallel plates of equal and opposite charge.

3 Review: Work and Energy Work is defined as the product of displacement x and a parallel applied force F. Work = Fx; Units: 1 J = 1 N m Potential Energy, U, is defined as the ability to do work by virtue of position or condition. (Joules) Kinetic Energy, K, is defined as the ability to do work by virtue of motion (velocity). (Joules)

4 Signs for Work and Energy Work (Fx) is positive if an applied force, F, is in the same direction as the displacement, x. B A F P mg x The force, F, does positive work. The force, mg, does negative work. The P.E. at B relative to A is positive because the field can do positive work if object P is released. P.E. at A relative to B is negative; outside force needed to move object P from A to B.

5 Gravitational Work and Energy Consider work against g to move object P from A to B, a vertical height h. Work = Fh = mgh At level B, the potential energy U is: U = mgh (gravitational) The external force does positive work; the gravity, g, does negative work. B F P mg A h g The external force, F, against the gravity field increases the potential energy, U.

6 Electrical Work and Energy An external force, F e, moves a +q charge from A to B against the electric field force, qe, (from F e = qe). Work = Fx = (qe)d At level B, the potential energy, U is: U = qed (Electrical) The Electric field does negative work. The external force does positive work. B F e +q d (x) qe E A The external force, F e, against the Electric field increases the potential energy.

7 Electric Potential Difference Since work depends on the magnitude of the charge, q e, we can define this in terms of energy per charge by dividing both sides of the equation, U = Fd, by the charge q e. U q W q Volt J / C The electrical potential energy is measured in Joules. It can also be measured in another term called the electron Volt, ev. 1eV = 1.60 x J

8 Electric Potential Difference One electron volt is the magnitude of the amount by which the potential energy of an electron changes when the electron moves through a potential difference of one volt. W or Potential Energy (U) qv As you can see, there must be a difference in potential for there to be voltage. So we can define another name for voltage as POTENTIAL DIFFERENCE. The potential here however is caused by an electric force which is related to electric energy. This is important to understand! A FORCE drives the +q DOWNWARD and it also covers a DISPLACEMENT.

9 Electric Potential Difference Therefore, if we consider the definition for WORK, and use it algebraically, a new relationship for the Voltage results. V E V we get V E avg U q F q Eqx q E e and U avg, solve the same V - d d,or for Ed, if Fx, sov F d e final and x,and Fe x q sub in above, or equation,and sub in E you get for F q e,

10 Parallel Plates Consider Two parallel plates of equal and opposite charge, a distance d apart. Constant E field: F = qe V A q d E Work = Fd = (qe)d Also, Work = q(v A V B ) V B So that: qv AB = qed, so: V AB = Ed or E = V/d The potential difference between two oppositely charged parallel plates is the product of E and d.

11 Example 1. (a) Calculate the speed of a proton that is accelerated from rest through a potential difference of 120 V. (b) Calculate the speed of an electron that is accelerated through the same potential difference. Answer: a x 10 5 m/s; b x 10 6 m/s

12 Example 2. A deuteron (a nucleus which consists of one proton and one neutron) is accelerated through a 2.7 kv potential difference. (a) How much energy does it gain? (b) (b) How fast would it be going if it started from rest? Answer: a x J b x 10 5 m/s

13 Example 3. An ion accelerated through a potential difference of 115 V experiences an increase in kinetic energy of 7.37 x J. Calculate the charge on the ion. Answer: 6.41 x C

14 Example 4. A positron, when accelerated from rest between two points at a fixed potential difference, acquires a speed of 30% of the speed of light. What speed will be achieved by a proton if accelerated from rest between the same two points? Answer: 2.10 x 10 6 m/s

15 Example 5. The electric field between two charged parallel plates separated by a distance of 1.8 cm has a uniform value of 2.4 x 10 4 N/C. Find the potential difference between the two plates. How much kinetic energy would be gained by a deuteron in accelerating from the positive to the negative plate? Answer: 6.92 x J or 432 ev

16 Example 6. A proton moves in a region of uniform electric field. The proton experiences an increase in kinetic energy of 5 x J after being displaced 2 cm in a direction parallel to the field. What is the magnitude of the electric field? Answer: 1.56 x 10 3 N/C

17 Electric Potential Difference Created by Point Charges Recall that work is force times a distance, substitute this in for work. W F ex V, x r, and Then substitute the q q electrical force formula kq 1q F 2 e, sub into formula above, in for force and you get 2 r the formula for finding kq1q 2 the Potential of a point r 2 kq r 1q2r kq V 1 charge at a given point, or q 2 r q r from a charge or set of charges. q Total Voltage (V) k i r i

18 Potential For Multiple Charges When two or more charges are present, the potential due to all the charges is obtained by adding together the individual potentials. Q 1 r 1 - A r 2 V A kq r 1 1 kq r 2 2 kq r 3 3 Q 3 - r 3 + Q 2 V k q r i BE CAREFUL, since voltage is potential difference, that means you add the signs. DO NOT USE THE ABSOLUTE VALUE of the equation! You must use the sign or signs of the charge or charges!

19 Example 7. At what distance from a point charge of 8 μc would the potential equal 3.6 x 10 4 V? Answer: 2.0 m

20 Example 8. At a distance r away from a point charge q, the electrical potential is V = 400 V and the magnitude of the electric field is E = 150 N/C. Determine the value of q and r. Answer: r = 2.67 m, q = 119 nc

21 Example 9. The three charges shown in the figure are at the vertices of an isosceles triangle. Calculate the electric potential at the midpoint of the base, taking q = 7 μc. Answer: x 10 7 V

22 Example 10. Two point charges, Q 1 = +5 nc and Q 2 = -3 nc, are separated by 35 cm. (a) What is the potential energy of the pair? What is the significance of the algebraic sign of your answer? (b) What is the electric potential at a point midway between the charges? Answer: (a) x 10-7 J, Energy needed to separate them. (b) V

23 Assignment Pages , #1, 5, 8, 13, 18, 27, 35, 38