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Unformatted text preview: ombs (C). We will replace the
prefix µ with 10−6 when calculating the distance r from Equation 18.1.
SOLUTION Solving F = k r2 = k q1 q2
r2 q1 q2
F (Equation 18.1) for the distance r, we obtain or r= k q1 q2
F Chapter 18 Problems 949 Therefore, when the force magnitude F is 0.66 N, the distance between the charges must be r= k 9. q1 q2
F = (8.99 × 10 9 N ⋅ m /C
2 2 ) (8.4 × 10−6 C ) ( 5.6 ×10−6 C ) = 0.80 m
0.66 N SSM REASONING The number N of excess electrons on one of the objects is equal to the charge q on it divided by the charge of an electron (−e), or N = q/(−e). Since the charge
on the object is negative, we can write q = − q , where q is the magnitude of the charge.
The magnitude of the charge can be found from Coulomb’s law (Equation 18.1), which
states that the magnitude F of the electrostatic force exerted on each object is given by
F = k q q / r 2 , where r is the distance between them.
SOLUTION The number N of excess electrons on one of the objects is
e (1) To find the magnitude of the charge, we solve Coulomb’s law, F = k q q / r 2 , for q :
q= F r2
k Substituting this result into Equation (1) gives ( 4.55 ×10 N )(1.80 ×10 m )
8.99 ×109 N ⋅ m 2 / C2
1.60 × 10−19 C
−21 −3 2 10. REASONING The gravitational force is an attractive force. To neutralize this force, the
electrical force must be a repulsive force. Therefore, the charges must both be positive or
both negative. Newton’s law of gravitation, Equation 4.3, states that the gravitational force
depends inversely on the square of the distance between the earth and the moon. Coulomb’s
law, Equation 18.1 states that the electrical force also depends inversely on the square of the
distance. When these two forces are added together to give a zero net force, the distance
can be algebraically eliminated. Thus, we do not need to know the distance between the
two bodies. 950 ELECTRIC FORCES AND ELECTRIC FIELDS SOLUTION Since the repulsive electrical force neutralizes the attractive gravitational
force, the magnitudes of the two forces are equal:
kqq = 2 1 24
Equation 18.1 GM e M m
Equation 4.3 Solving this equation for the magnitude q of the charge on either body, we find
2 −11 N ⋅ m 5.98 × 1024 kg 7.35 × 1022 kg 6.67 × 10
GM e M m
= 5.71 × 1013 C
8.99 × 109
______________________________________________________________________________ ( 11. )( ) SSM WWW REASONING Initially, the two spheres are neutral. Since negative
charge is removed from the sphere which loses electrons, it then carries a net positive
charge. Furthermore, the neutral sphere to which the electrons are added is then negatively
charged. Once the charge is transferred, there exists an electrostatic force on each of the
two spheres, the magnitude of which is given by Coulomb's law (Equation 18.1),
F = k q1 q2 / r 2 .
a. Since each electron carries a charge of −1.60 ×10−19 C , the amount of negative charge
removed from the first sphere is 1.60 ×10−19 C −6
3.0 ×1013 electrons 1 electron = 4.8 ×10 C ( ) Thus, the first sphere carries a charge +4.8 × 10–6 C, while the second sphere carries a
charge −4.8 × 10–6 C. The magnitude of the electrostatic force that acts on each sphere is,
therefore, F= k q1 q2
r2 (8.99 ×109 N ⋅ m2 /C2 ) ( 4.8 ×10−6 C)
( 0.50 m )2 2 = 0.83 N b. Since the spheres carry charges of opposite sign, the force is attractive .
______________________________________________________________________________ Chapter 18 Problems 12. REASONING Let F2 and F1 represent the forces exerted on the
charge q at the origin by the point charges q1 and q2, respectively.
According to Equation 18.1, the magnitudes of these forces are
given by F1 = k q1 q F2 = k and r12 951 y
q1 = −25 µC q2 q (1) r22 F1 where r1 is the distance between q1 and q, r2 is the distance q = +8.4 µC
between q2 and q, and k = 8.99×109 N·m2/C2. The directions of
the forces are determined by the signs of each charge-pair. The F2
sign of q1 is opposite that of q, so F1 is an attractive force,
pointing in the positive y direction. The signs of q2 and q are both
positive, so F2 is a repulsive force, pointing in the negative y direction (see the drawing).
Because the net force F = F1 + F2 acting on q points in the positive y direction, the force F1
must have a greater magnitude than the force F2. Therefore, the magnitude F of the net
electric force acting on q is equal to the magnitude of the attractive force F1 minus that of
the repulsive force F2:
F = F1 − F2 (2) SOLUTION Substituting Equations (1) into Equation (2) yields
F = F1 − F2 = k q1 q
r12 −k q2 q (3) r22 Solving Equation (3) for |q2|, we obtain
k q2 q
r22 =k q1 q
r12 −F or q
q2 = r22 1 − r2 k q
1 Substituting the given values, we find that −25 × 10 −6 C 27 N = 1.8 × 10 −5 C
q2 = ( 0.34...
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