Physics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/1

Transcription

1 Physics 201 p. 1/1 Physics 201 Professor P. Q. Hung 311B, Physics Building

2 Physics 201 p. 2/1 Summary of last lecture Force on a point charge q 0 in the presence of an electric field: F = q 0 E(r)

3 Physics 201 p. 2/1 Summary of last lecture Force on a point charge q 0 in the presence of an electric field: F = q 0 E(r) E(r) can be calculated using either Coulomb s law or Gauss s law.

4 Physics 201 p. 2/1 Summary of last lecture Force on a point charge q 0 in the presence of an electric field: F = q 0 E(r) E(r) can be calculated using either Coulomb s law or Gauss s law. From last semester, a Force does Work. Furthermore, Conservative Force (like e.g. 1/r 2 force) Concept of Potential Energy and Concept of Potential.

5 Physics 201 p. 3/1 Electric Potential Energy Recall that the gravitational force is F g = G m 1 m 2 r 2 and it is a conservative force A potential energy is associated with it.

6 Electric Potential Energy Recall that the gravitational force is F g = G m 1 m 2 r 2 and it is a conservative force A potential energy is associated with it. The work done by gravity: from point A to point B is (positive direction pointing upward): W AB = KE B KE A = U A g U B g = mgh A mgh B Physics 201 p. 3/1

7 Physics 201 p. 4/1 Electric Potential Energy An electric force does work W AB = J in moving a charge q 0 = +2.0µC from A to B. 1) Find the potential energy difference; 2) Find the potential difference between B and A. How does one goes from the work done by an electric force to the potential energy difference?

8 Physics 201 p. 4/1 Electric Potential Energy An electric force does work W AB = J in moving a charge q 0 = +2.0µC from A to B. 1) Find the potential energy difference; 2) Find the potential difference between B and A. How does one goes from the work done by an electric force to the potential energy difference? What is the potential difference?

9 Physics 201 p. 5/1 Electric Potential Energy U e Force on +q: F = q E. Assume a uniform electric field E pointing vertically downward.

10 Physics 201 p. 5/1 Electric Potential Energy U e Force on +q: F = q E. Assume a uniform electric field E pointing vertically downward. Work done by this force in moving the particle from A to B with h A > h B : W AB = q E h A q E h B = KE B KE A

11 Physics 201 p. 5/1 Electric Potential Energy U e Force on +q: F = q E. Assume a uniform electric field E pointing vertically downward. Work done by this force in moving the particle from A to B with h A > h B : W AB = q E h A q E h B = KE B KE A Conservative electric force W AB = q E h A q E h B = KE B KE A = Ue A U e B

12 Physics 201 p. 6/1 Electric Potential Energy

13 Physics 201 p. 7/1 Electric Potential: Electric Potential V = U e q Unit: V = joule/coulomb=volt

14 Physics 201 p. 7/1 Electric Potential: Electric Potential V = U e q Unit: V = joule/coulomb=volt Notice that V is not a vector. It is a scalar

15 Physics 201 p. 7/1 Electric Potential: Electric Potential V = U e q Unit: V = joule/coulomb=volt Notice that V is not a vector. It is a scalar potential difference between B and A is: V B V A = U B e q U A e q = W AB q = E(h A h B ) < 0

16 Physics 201 p. 8/1 More generally: Electric Potential V B V A = E. s where s is the displacement vector pointing from A to B. The positive charge which moves in the direction of the electric field, goes from high to low potential. How about negative charge?

17 Physics 201 p. 8/1 More generally: Electric Potential V B V A = E. s where s is the displacement vector pointing from A to B. The positive charge which moves in the direction of the electric field, goes from high to low potential. How about negative charge? IMPORTANT POINT: As with the gravitational case, only the potential energy and potential difference makes physical sense.

18 Physics 201 p. 9/1 Electric Potential

19 Physics 201 p. 10/1 Electric Potential An electric force does work W AB = J in moving a charge q 0 = +2.0µC from A to B. 1) Find the potential energy difference; 2) Find the potential difference between B and A. U B e U A e = W AB = J < 0. The potential energy is higher at A than at B.

20 Physics 201 p. 10/1 Electric Potential An electric force does work W AB = J in moving a charge q 0 = +2.0µC from A to B. 1) Find the potential energy difference; 2) Find the potential difference between B and A. U B e U A e = W AB = J < 0. The potential energy is higher at A than at B. V B V A = W AB /q = J +2.0µC = 25 V. So V B < V A.

21 Physics 201 p. 11/1 Electric Potential A 12-V battery powers a 60.0 W headlight for one hour. How many electrons have passed through the terminals of the battery during that time? Energy consumed by the headlight in one hour: Energy = Power x time E = 60.0W 3600s = J.

22 Physics 201 p. 12/1 Electric Potential Equal to the change in potential energy of the total number of electrons which pass through the terminals: E = Q V = Q12V = J Q = C.

23 Physics 201 p. 12/1 Electric Potential Equal to the change in potential energy of the total number of electrons which pass through the terminals: E = Q V = Q12V = J Q = C. Each electron carries a charge of magnitude C. The total number of electrons is N = C C =

24 Conservation of Energy Point B has an electric potential that is 25 V greater than that of point A. A particle of mass kg and a charge whose magnitude is C. We will neglect gravity and friction. (a) If the particle has a positive charge and is released from rest at B, what speed v A does the particle have when it arrives at A? (b) If the particle has a negative charge and is released from rest at A, what speed v B does the particle have when it arrives at B? (c) What if the negatively charged particle is released from rest from B? Physics 201 p. 13/1

25 Physics 201 p. 14/1 Conservation of Energy (a) 1 2 mv2 A + qv A = 1 2 mv2 B + qv B. 1 2 mv2 A = q(v B V A ) v A = = 9.1 m/s. 2q(V B V A ) m

26 Physics 201 p. 14/1 Conservation of Energy (a) 1 2 mv2 A + qv A = 1 2 mv2 B + qv B. 1 2 mv2 A = q(v B V A ) v A = = 9.1 m/s. 2q(V B V A ) m (b) A negatively charged particle accelerating from rest from A is the same as a positively charged particle accelerating from rest from B v B = 9.1m/s.

27 Physics 201 p. 14/1 Conservation of Energy (a) 1 2 mv2 A + qv A = 1 2 mv2 B + qv B. 1 2 mv2 A = q(v B V A ) v A = = 9.1 m/s. 2q(V B V A ) m (b) A negatively charged particle accelerating from rest from A is the same as a positively charged particle accelerating from rest from B v B = 9.1m/s. (c) It will never reach B.

28 Physics 201 p. 15/1 Conservation of Energy Another unit of energy: ev or electronvolt. One ev is the change in potential energy of an electron moving a potential difference of one volt.

29 Physics 201 p. 15/1 Conservation of Energy Another unit of energy: ev or electronvolt. One ev is the change in potential energy of an electron moving a potential difference of one volt. 1 ev = J.

30 Physics 201 p. 16/1 Electric Potential of a point charge A charge q 1 = 2.00µC is located at the origin and a charge q 2 = 6.00µC is located at (0, 3.00 m). Find the total electric potential at point P situated at (4.00m, 0). See the figure drawn in class. The electric field of a point charge is not constant. We cannot use the formula derived above.

31 Physics 201 p. 16/1 Electric Potential of a point charge A charge q 1 = 2.00µC is located at the origin and a charge q 2 = 6.00µC is located at (0, 3.00 m). Find the total electric potential at point P situated at (4.00m, 0). See the figure drawn in class. The electric field of a point charge is not constant. We cannot use the formula derived above. So what s the electric potential of a point charge then?

32 Physics 201 p. 17/1 Electric Potential of a point charge E(r) = k q r 2 ˆr (NOT CONSTANT) V B V A = B A E.d s = k q r B k q r A

33 Physics 201 p. 17/1 Electric Potential of a point charge E(r) = k q r 2 ˆr (NOT CONSTANT) V B V A = B A E.d s = k q r B k q r A Boundary condition: V A = 0 when r A is infinite:

34 Physics 201 p. 17/1 Electric Potential of a point charge E(r) = k q r 2 ˆr (NOT CONSTANT) V B V A = B A E.d s = k q r B k q r A Boundary condition: V A = 0 when r A is infinite: V = k q r

35 Physics 201 p. 18/1 Electric Potential of a point charge

36 Physics 201 p. 19/1 Electric Potential of a point charge A charge q 1 = 2.00µC is located at the origin and a charge q 2 = 6.00µC is located at (0, 3.00 m). Find the total electric potential at point P situated at (4.00m, 0). See the figure drawn in class. The individual potentials add like scalars

37 Physics 201 p. 19/1 Electric Potential of a point charge A charge q 1 = 2.00µC is located at the origin and a charge q 2 = 6.00µC is located at (0, 3.00 m). Find the total electric potential at point P situated at (4.00m, 0). See the figure drawn in class. The individual potentials add like scalars The distance between q 1 and P is 4.00 m. The distance between q 2 and P is 5.00 m.

38 Electric Potential of a point charge A charge q 1 = 2.00µC is located at the origin and a charge q 2 = 6.00µC is located at (0, 3.00 m). Find the total electric potential at point P situated at (4.00m, 0). See the figure drawn in class. The individual potentials add like scalars The distance between q 1 and P is 4.00 m. The distance between q 2 and P is 5.00 m. V P = k( q 1 r 1 + q 2 r 2 ) V P = N.m2 C C ( m C 5.00m ) = V. Physics 201 p. 19/1