Assume that you have two objects, one with a mass of 5 kg and the other with a mass of 20 kg, each with a charge of −0.012 C and separated by a distance of 9m.
What is the electric force that these objects exert on one another?
Answer in units of N
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To calculate the electric force between the two objects, 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.
The formula for Coulomb's Law is:
F = k * (|q1 * q2|) / r^2
where:
F is the electric force
k is the electrostatic constant, approximately equal to 9.0 x 10^9 N m²/C²
q1 and q2 are the charges of the objects
r is the distance between the centers of the objects
In this case, q1 and q2 are both -0.012 C, and r is 9 m. Substituting these values into the formula, we get:
F = (9.0 x 10^9 N m²/C²) * (|(-0.012 C) * (-0.012 C)|) / (9 m)^2
Calculating the expression inside the brackets first:
|(-0.012 C) * (-0.012 C)| = (0.012 C) * (0.012 C) = 0.000144 C²
Now, substituting this value and the other given values into the formula:
F = (9.0 x 10^9 N m²/C²) * (0.000144 C²) / (9 m)^2
Next, simplify:
F = (9.0 x 10^9 N m²/C²) * (0.000144 C²) / 81 m²
Now calculate the numerator:
(9.0 x 10^9 N m²/C²) * (0.000144 C²) = 1.296 x 10^6 N m² / C²
Finally, substitute this value and the value of the denominator into the formula:
F = 1.296 x 10^6 N m² / C² / 81 m²
Now, divide the numbers:
F = 1.296 x 10^6 N m² / C² / 81 m² = 1.6 x 10^4 N
So, the electric force that these objects exert on one another is 1.6 x 10^4 N.