The force between a pair of [tex]0.001 \, \text{C}[/tex] charges is [tex]200 \, \text{N}[/tex]. What is the distance between them?
Answer (3)
From Columb's Law which describe the electrostatic interaction. The formula is given and looks as follows F = k r 2 ∣ q 1 ∗ q 2∣ where: F is force acting between charges, q1 - charge one given in columbs, q2 - charge two given in columbs, r - distance between charge in meters k - constant
First, we have to convert out formula to get r. F = k r 2 q 1 ∗ q 2 Now we multiplaty by r 2 both sides of equation F ∗ r 2 = k ∗ ∣ q 1 ∗ q 2∣ Now we devide both sides by F r 2 = k F ∣ q 1 ∗ q 2∣ Next step is take square root r = k F ∣ q 1 ∗ q 2∣ We have all date, we can subsitute it to our formula r = k ∗ F ∣ q 1 q 2" = 2 8.9 ∗ 1 0 9 ∗ 200 0.001 ∗ 0.001 = 6.67 [ m ]
Using Coulomb's Law, the distance between two charges of 0.001 C each, experiencing a force of 200 N, is calculated to be approximately 6.70 meters.
To determine the distance between two charges, we can use Coulomb's Law, which states that the force between two charges (F) is directly proportional to the product of the charges and inversely proportional to the square of the distance between them (r). The equation is:
Coulomb's Law: F = k * ( q 1 * q 2 ) / r²
Given:
q 1 = 0.001 C
q 2 = 0.001 C
F = 200 N
k (Coulomb's constant) = 8.99 × 10⁹ N·m²/C²
We need to find the distance (r) between the charges. Rearranging the formula to solve for r gives:
r = \sqrt ( k * ( q 1 * q 2 ) / F )
Substituting the given values:
r = \sqrt (.99 × 10⁹ * (0.001 * 0.001) / 200 )
r = \sqrt ( 8.99 × 10⁹ * 1 × 10⁻⁶ / 200 )
r = \sqrt ( 8.99 × 10³ / 200 )
r = \sqrt ( 44.95 )
r ≈ 6.70 meters
Thus, the distance between the two charges is approximately 6.70 meters.
Using Coulomb's Law, the distance between the two charges of 0.001 C each that exert a force of 200 N on each other is calculated to be approximately 6.7 meters. The formula used is r = k F ∣ q 1 q 2 ∣ . By substituting the given values, we arrive at this distance.
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