Two identical small spherical conductors (point charges), separated by 0.6 m, carry a total charge of 200 mu or micro CC. They repel one another with a force of 120 N. (For the universal constant k use the value 8.99 times 109 N m2/C2.)
so I used q1 + q2= 200e-6C
and q1*q2= Fr^2/k I solved for q1*q2 and plugged q1=200e-6 - q2 into that equation. used the quadratic formula and got q2 to be 200uC but this logically does not make sense because then q1 would have to be 0uC.
To solve this problem, you correctly started with the equation q1 + q2 = 200 μC, which represents the total charge on both conductors.
Next, you used the equation q1*q2 = (F * r^2) / k, where F is the repulsive force of 120 N, r is the separation distance of 0.6 m, and k is the universal constant.
You correctly rearranged the equation to solve for q1*q2. Substituting q1 = 200 μC - q2, you obtained:
(200 μC - q2) * q2 = (120 N * (0.6 m)^2) / (8.99 x 10^9 N m^2/C^2)
However, when you used the quadratic formula, you arrived at the result q2 = 200 μC, which seems illogical because it would imply that q1 is 0 μC.
To address this issue, it's important to consider the physical properties of charging and matter conservation. In this case, the two conductors have identical charges, so their charges are equal, i.e., q1 = q2.
To resolve the equation, let's revisit the equation q1 + q2 = 200 μC. Since q1 = q2, we can rewrite the equation as:
2q = 200 μC
Dividing both sides by 2, we get:
q = 100 μC
Therefore, each conductor has a charge of 100 μC.
It's important to note that in some cases, the quadratic equation would have provided multiple solutions. However, in this particular scenario, the physical constraints of identical charges limit the solution to q = 100 μC for each conductor.