(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two identical small metal spheres with q1 > 0

and |q1| > |q2| attract each other with a force

of magnitude 70.2 mN, as shown.

The spheres are then brought together until

they are touching. At this point, the spheres

are in electrical contact so that the charges

can move from one sphere to the other until

both spheres have the same ﬁnal charge, q.

After the charges on the spheres have come

to equilibrium, the spheres are moved so that

they are again 1.87 m apart. Now the spheres

repel each other with a force of magnitude

18.954 mN.

Returned to original position

A.)What is the ﬁnal charge on sphere 2? The Coulomb

constant is 8.98755 × 10^9N m2/C2

.Answer in units of µC

002 (part 2 of 2) 10.0 points

B.)What is the initial charge q1 on the ﬁrst

sphere?

Answer in units of µ

2. Relevant equations

F=kq1q2/r^2

x=-b(+/-)sqrt(b^2-4ac)/2a

3. The attempt at a solution

q1 is positive, q2 is negative

F 12 = F 21 = 70.2 mN = -k(q1)(q2)/r²

k = 1/((4)(π)(ε) = 8.9876 x 10^9 m²/c²

70.2mN = -(8.9876 x 10^9)(q1)(q2)/1.87²

after the spheres touch the charge on each sphere is qf = (q1 +q2)/2

F = 18.954 x 10^-3 = (8.9876 x 10^9)(qf²)/1.87²

qf = 2.716 uC

A) 2.716 uC

q1 = -q2 + 2*qf

q1 = -q2 +5.432uC

q1(q2) = 2.73 x10^-11

-q2² + (5.43 x 10^-6)q2 +2.73 x 10^-11 = 0

q2= -+2716 x 10^-6 +/- sqrt(2.95 x 10^-11 + 4(2.73 x 10^-11))/4 = +2.716 +/- 2.944 uC

q2 is negative , so -.288 uC

q1= 5.72 uC

B).?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Finding the initial and final charge of two spheres

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