Two spherical objects are separated by a distance that is 9.00 10-3 m. The objects are initially electrically neutral and are very small compared to the distance between them. Each object acquires the same negative charge due to the addition of electrons. As a result, each object experiences an electrostatic force that has a magnitude of 4.5500 10-21 N. How many electrons did it take to produce the charge on one of the objects?
the equation is F=1/ (4pi episilon) times q1*q2/ r^2)
r is distance
f is force
q1 and 2 are charges.
i have wrestled with this problem.
i made it to the step where i got q1q2= 4.0995X10^-35
from here i am stuck
could someone do this problem for me and lay the steps out and explain where and why the steps are done?
the equation is F=1/ (4pi episilon) times q1*q2/ r^2)
r is distance
f is force
q1 and 2 are charges.
i have wrestled with this problem.
i made it to the step where i got q1q2= 4.0995X10^-35
from here i am stuck
could someone do this problem for me and lay the steps out and explain where and why the steps are done?
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The problem states that the objects are given equal charge, that's why q1 = q2. This equal charge we can denote q and therefore q1 q2 = q q = q^2
q^2 = 4 pi Eo r^2 F
q = - sqrt(4 pi Eo r^2 F) [[ choose minus (-) because we are told that a negative charge is applied]
Dividing by the charge per electron (- e , where e is the elementary charge 1.602 10^-19 C ) we have for the number of electrons on one object N:
N = q/(-e) = sqrt(4 pi Eo r^2 F) / e
q^2 = 4 pi Eo r^2 F
q = - sqrt(4 pi Eo r^2 F) [[ choose minus (-) because we are told that a negative charge is applied]
Dividing by the charge per electron (- e , where e is the elementary charge 1.602 10^-19 C ) we have for the number of electrons on one object N:
N = q/(-e) = sqrt(4 pi Eo r^2 F) / e
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Dr Zorro's answer is correct, but your E0 isn't - it's a constant = 8.85 * 10^-12 and it is called the Permittivity of Free Space.
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I see you are using MKS to solve an electrostatic problem but I see no constants being used. MKS is a non rational system of measurements that requires corrective numerical inserts in order for any such equation to make sense. These are the permittivity and permeabilty of space. If you swicth to cgs which is completely rational, then you will need no constants and you will understand the situation better. MKS confuses and blinds those who use it. The international volt does not belong to MKS and was grafted on with those constants. The cgs system uses the Statvolt and needs no corrective numerical inserts to be right, it just IS right. Only amateurs use MKS for an electrostatic problem, step up to greater understanding.