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Lecture 8 Examples & Problems

Lecture 8 Examples & Problems. Examples & Problems. Example 1: What potential difference is needed to stop an electron with an initial speed of 4.2*10 5 m/s?. W = Δk = k f - k i W = 0-k i q V = -1/2 mv 2 V = -(1/2 mv 2 ) / q V = -(1/2 x 9.1x10 -31 x(4.2x105)2)/1.5x10 -19 V = -0.57 volt.

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Lecture 8 Examples & Problems

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  1. Lecture 8 Examples & Problems

  2. Examples & Problems Example 1: What potential difference is needed to stop an electron with an initial speed of 4.2*105m/s? W = Δk = kf - ki W = 0-ki q V = -1/2 mv2 V = -(1/2 mv2) / q V = -(1/2 x 9.1x10-31x(4.2x105)2)/1.5x10-19 V = -0.57 volt Example 2:An ion accelerated through a potential difference of 115V experiences an increase in potential energy of 7.37*10-17J. Calculate the charge on the ion. VB - VA = Wab/ q q = Wab/ VB - VA q= 6.41x10-19C

  3. Example 3:An infinite charged sheet has a surface charge density s of 1.0*10-7 C/m2.  How far apart are the equipotential surfaces whose potentials differ by 5.0 V? E = 1.0´10-7/(2x8.85x10-12)= 5650 N/C V = Ed d = V/E d = 8.8x10-4m Example 4:At what distance from a point charge of 8mC would the potential equal 3.6*104V? r = 2 m

  4. Example 5:At a distance r away from a point charge q, the electrical potential is V=400v and the magnitude of the electric field is E=150N/C.  Determine the value of q and r. r = 2.67m

  5. Example 6:Calculate the value of the electric potential at point P due to the charge configuration shown in Figure 5.19. Use the values q1=5mC, q2=-10mC, a=0.4m, and b=0.5m. V = V1 + V2 + V3 + V4 Example 7:Two large parallel conducting plates are 10cm apart and carry equal and opposite charges on their facing surfaces.  An electron placed midway between the two plates experiences a force of 1.6*1015N.  What is the potential difference between the plates? V=Ed E = F/q V = (F/q) d V = (1.6x1015/1.6x10-19) x 0.05 = 5x1032v

  6. Example 8:Two point charges are located as shown in, where ql=+4mC, q2=-2mC, a=0.30m, and b=0.90m. Calculate the value of the electrical potential at points P1, and P2.  Which point is at the higher potential? Vp1 = V1 + V2

  7. Example 9: In figure 5.22 prove that the work required to put four charges together on the corner of a square of radius a is given by  (w=-0.21q2/eoa). U = U12 + U13 + U14 + U23 + U24 + U34

  8. Example • Assume we have a system of three point charges:q1 = +1.50 Cq2 = +2.50 Cq3 = -3.50 C. • q1 is located at (0,a)q2 is located at (0,0)q3 is located at (b,0)a = 8.00 m and b = 6.00 m. • What is the electric potential at point P located at (b,a)?

  9. r1 • The electric potential at point P is given by the sum of the electric potential from the three charges r2 r3

  10. (1) Two charges q=+2*10-6C are fixed in space a distance d=2cm apart, as shown in figure (a) What is the electric potential at point C? (b) You bring a third charge qn=2.0*10-6C very slowly from infinity to C.  How much work must you do?  (c) What is the potential energy U of the configuration when the third charge is in place? (2) Four equal point charges of charge q=+5mC arelocated at the corners of a 30cm by 40cm rectangle. Calculate the electric potential energy stored in this charge configuration. (3) Two point charges, Q1=+5nC and Q2=-3nC, are separated by 35cm. (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?

  11. (4) What is the potential at the center of the square shown in figure 5.9? Assume thatq1= +1 ´10-8C,  q2= -2´10-8C,  q3=+3´10-8C, q4=+2´10-8C, and a=1m. (5) Two charges of 2mC and -6mC are located at positions (0,0) m and (0,3) m, respectively as shown in figure.  (i) Find the total electric potential due to these charges at point (4,0) m.  (ii) How much work is required to bring a 3mC charge from ¥ to the point P?  (iii) What is the potential energy for the three charges?

  12. (6) A particle having a charge q=3*10-9C moves from point a to point b along a straight line, a total distance d=0.5m.  The electric field is uniform along this line, in the direction from a to b, with magnitude E=200N/C.  Determine the force on q, the work done on it by the electric field, and the potential difference Va-Vb. (7) For the charge configuration shown in figure , Show that V(r) for the points on the vertical axis, assuming r >> a, is given by

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