Question

Q1=2нКл q2=5нКл F=9мН Найти:r-?

Answer 1

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Answer 2

To find the distance (r) between two charges (q1 and q2) given the force (F) between them, you can use Coulomb's law, which describes the relationship between the electric force and the distance between charges. The formula is:

$F = \frac{k \cdot |q_1 \cdot q_2|}{r^2}$

where: F = Force between the charges (in Newtons, N) k = Coulomb's constant, approximately 8.99 x 10^9 Nm²/C² q1, q2 = Magnitudes of the charges (in Coulombs, C) r = Distance between the charges (in meters, m)

Now, let's plug in the given values:

q1 = 2nC = 2 x 10^(-9) C q2 = 5nC = 5 x 10^(-9) C F = 9mN = 9 x 10^(-3) N k = 8.99 x 10^9 Nm²/C²

$9 \times 10^{-3} N = \frac{8.99 \times 10^9 Nm^2/C^2 \cdot |2 \times 10^{-9} C \cdot 5 \times 10^{-9} C|}{r^2}$

Now, let's solve for r:

$r^2 = \frac{8.99 \times 10^9 Nm^2/C^2 \cdot 2 \times 10^{-9} C \cdot 5 \times 10^{-9} C}{9 \times 10^{-3} N}$

$r^2 = \frac{8.99 \times 2 \times 5 \times 10^{-9} \times 10^{-9} \times 10^9 \times 10^{-9}}{9}$

$r^2 = \frac{89.9 \times 10^{-9}}{9}$

$r^2 = 9.99 \times 10^{-9}$

$r = \sqrt{9.99 \times 10^{-9}}$

$r \approx 3.16 \times 10^{-5}$

So, the distance (r) between the charges is approximately 3.16 x 10^-5 meters, or 31.6 micrometers.