Giancoli 5th Ed.

Hwk 4 (Due Mon 9/19)
Ch. 23 P. 2,3,5,9,12,15,17,21,25,28,29,35,36,43,48,51
       MCQ. 1-13 (odd)

Problems: 
2. W_ba = -qV_ba = 3.04e-17 J  or 1.9e+2 eV
3. Delta V = -(Delta K)/q = -0.77 V
5. a) ma = qE, so a = qE/m 
      Also use v_f^2 = v_i^2 = 2a(x_f-x_i) to find
          (x_f-x_i) = Delta x = 1.9e-7 m
   b) q(Delta V) = K_f = 1/2 m(v_f)^2
      so Delta V = 1.1e-3 V
9. E = (V_ba)/d   so d = 2.8e-2 m
12. V_surf = r(E_breakdown) so r = V/E = 0.015m
    V_surf = kQ/r  so Q = rV/k  = 7.5e-8 C
15. a)  V = E(r_Earth) = (-150 V/m)(r_Earth) = -9.6e+8 V
    b) If we define V=0 at r_Earth, then at r=infty V=+9.6e+8 V.
       If we keep V=0 at infinity but add a shell of + charge
       above the surface (with the same magnitude as the charge 
       on the surface), then the E above the ionosphere is 0
       (by Gauss's law).  The potential at the Earth's surface
       would then have a smaller magnitude but still have a 
       negative sign.
17. a) the two spheres are at the SAME potential
    b) The potentials of the two spheres are still equal,
       but their charges will differ.
           V_1=V_2  so kQ_1/r_1 = kQ_2/r_2  but Q_2=Q-Q_1.
             so Q_1 = Q(r_1/[r_1+r_2])
       charge transferred = Q-Q_1 = Q(r_2/[r_1+r_2])
21. a) V_BA = 0  The line between the 2 points is perpendicular to E.
    b) V_CB = V_C - V_B = -44.1 V
    c) V_CA = V_C - V_A = V_CB + V_BA = -44.1 + 0 = -44.1 V
25. V = kQ/r so Q = 2.8e-9 C
28. V_corner = V_3 + V_1 + V_-2
             = k(3Q)/l  + k(Q)/(l*sqrt(2)) + k(-2Q)/l
             = k (sqrt(2)/2) * Q/l * (sqrt(2)+1)
29. W_ext = U_fin - U_in      Let D=6cm, d=1cm.
          = 2KQq[1/(D-2d) + 1/(D+2d) + 1/(D/2)]
          = 0.28 J
35  V = K int { dq/r }  where dq = sigma(2*pi*R*dR)
    V = sigma/2{eps_0} [sqrt(x^2+R_2^2) - sqrt(x^2+R_1^2)]
36. V = K int { dq/r }  over the semicircle
    V = k Q / r_0  but r_0 = l/pi  so
    V = k Q pi/l   (or V = Q/4*e_0*l )
43. Delta V = - E*(Delta x)   when E is uniform
    Delta x = x_0 - x_1
    E = sigma/e_0    for a metal plate (2 charged planes)
    so x_0 - x_1 = (Delta V0*e_0 / sigma) = 1.2e-3 m  (~1 mm)
48.  dV/dr = -E = -kq/r^2
      q = 92(1.6e-19 C)  and r=7.5e-15 m
     So dV/dr = -2.4e+21 V/m
51.  Ex = -dV/dx = -by+cyz,  Ey= -dV/dy = -2ay-bx+cxz
     Ez = -dV/dz = cxy
     So E = (-by+cyz)i +(-2ay-bx+cxz)j + (cxy)k

Misconceptual Questions
1. b
3. b
5. a
7. c
9. c
11. a
13. c


Please check
Prob.  
MiscQ