How close must two 1.0 C charged objects be for their mutual force to exceed 1.0 N? Compare that distance to something in your everyday life.
To determine the distance at which the mutual force between two charged objects exceeds 1.0 N, we can use Coulomb's Law. Coulomb's Law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Mathematically, Coulomb's Law can be expressed as:
F = (k * q1 * q2) / r^2
Where:
- F is the force between the two charged objects
- k is the electrostatic constant (approximately 9 × 10^9 N m^2/C^2)
- q1 and q2 are the charges of the objects in Coulombs (C)
- r is the distance between the objects
We want to find the distance between the objects when the force exceeds 1.0 N, so we rearrange the formula:
r = sqrt((k * q1 * q2) / F)
Considering that both objects have a charge of 1.0 C, we substitute q1 = q2 = 1.0 C:
r = sqrt((k * 1.0 C * 1.0 C) / 1.0 N)
r = sqrt(k / 1.0 N)
Now we can calculate the value of r:
r = sqrt(9 × 10^9 N m^2/C^2 / 1.0 N)
r = sqrt(9 × 10^9 m^2/C^2)
r = 3 × 10^4 m
The distance at which two 1.0 C charged objects would have a mutual force exceeding 1.0 N is approximately 3 × 10^4 meters.
To put it into perspective, this distance is quite large. It is roughly comparable to the height of Mount Everest, the highest peak on Earth, which is approximately 8.8 kilometers or 5.5 miles tall.
Not very close :)
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