2. (a) With a understood to mean the magnitude of acceleration, Newtons second and third laws lead to 6.3 107 kg 7.0 m s2 = 4.9 107 kg. m2 a2 = m1a1 m2 = 2 9.0 m s
c
hc
h
(b) The magnitude of the (only) force on particle 1 is
F = m1a1 = k q1 q2 r2 = ( 8.9
16. The total electric flux through the cube is = E dA . The net flux through the two faces parallel to the yz plane is
yz = [ Ex ( x = x2 ) Ex ( x = x1 ) ] dydz = = 6
y2 =1 y1 = 0 y2 =1 y1 = 0
dy
z2 = 3
z1 =1
dz [10 + 2(4) 10 2(1) ]
dy
z2 = 3
z1 =1
dz
55. We take the charge Q = 45.0 pC of the bee to be concentrated as a particle at the center of the sphere. The magnitude of the induced charges on the sides of the grain is | q | = 1.000 pC. (a) The electrostatic force on the grain by the bee is F= 1 kQq
43. (a) The magnitude of the force on the particle is given by F = qE, where q is the magnitude of the charge carried by the particle and E is the magnitude of the electric field at the location of the particle. Thus, E= F 3.0 106 N . = = 15 103 N C. q 2.
7. We assume the spheres are far apart. Then the charge distribution on each of them is spherically symmetric and Coulombs law can be used. Let q1 and q2 be the original charges. We choose the coordinate system so the force on q2 is positive if it is repe
5. The magnitude of the force of either of the charges on the other is given by F= 1 q Qq 4 0 r2
b
g
where r is the distance between the charges. We want the value of q that maximizes the function f(q) = q(Q q). Setting the derivative dF / dq equal to zer
4. The fact that the spheres are identical allows us to conclude that when two spheres are in contact, they share equal charge. Therefore, when a charged sphere (q) touches an uncharged one, they will (fairly quickly) each attain half that charge (q/2). W
3. The magnitude of the mutual force of attraction at r = 0.120 m is
F =k q1 q2 r2 = ( 8.99 10 N m C
9 2 2
)
( 3.00 10 C ) (1.50 10 C ) = 2.81N.
6 6
(0.120 m) 2
15. None of the constant terms will result in a nonzero contribution to the flux (see Eq. 23-4 and Eq. 23-7), so we focus on the x dependent term only: Enon-constant = (4.00y2 ) i (in SI units) . The face of the cube located at y = 4.00 has area A = 4.00