the unknowns are the charge of small and big charges are required

Question

 

 

 

Two small positively charged particles have a combined charge of 5.0 x 10-5 c . if each sphere are repelled from the other byAn electrostatic force of 1.0 N. when the spheres are 2.0 m apart . what is the charge on each sphere ?

Answer 1

To solve this problem we need to use Coulomb's Law:  F = (k Q ₁ Q ₂₎ / r ² , where k is a constant.

 

k = 9.0 x 10 ⁹ N·m²⁄C²

 

we are given:

 

F = 1.0 N

r = 2 m

 

Q ₁ + Q ₂ = 5.0 x 10 ^-5 C

 

Rearranging our equation for Coulomb's Law gives us:

 

Q ₁ x Q ₂ = (F x r²)/k = (1 N x 4 m²)/(9.0 x 10 ⁹ N·m²/C²) = 4.4 x 10 ^-10 C²

 

Since we know the sum of the two charges, we can write:

 

Q ₁ = 5.0 x 10 ^-5 C - Q ₂ 

 

Substituting for Q ₁ above gives:

 

(5.0 x 10 ^-5 C - Q ₂ ) x Q ₂ = 4.4 x 10 ^-10 C²

 

Then Q ₂^² - (5.0 x 10 ^-5)Q ₂ + 4.4 x 10 ^-10 = 0

 

Solve using the quadratic formula and we get:

 

Q (larger)   = 3.86 x 10 ^-5 C 

Q (smaller) = 1.14 x 10 ^-5 C