Question

Two equal charges are separated by 3.7 x 10^-10 m. The force between the charges has a magnitude of 2.37 x 10^-3 N. What is the magnitude of q on the charges?

Answer 1

Answer:

q= 1.9*10⁻¹⁶ C

Explanation:

To solve this problem we apply Coulomb's law:

Two point charges (q1, q2) separated by a distance (d) exert a mutual force (F) whose magnitude is determined by the following formula:

F=K*q₁*q₂/d² Formula (1)  

F: Electric force in Newtons (N)

K : Coulomb constant in N*m²/C²

q₁,q₂:Charges in Coulombs (C)  

d: distance between the charges in meters(m)

Data

F=2.37*10⁻³ N

K=8.99*10⁹N*m²/C²

q₁ = q₂=q

d= 3.7*10⁻¹⁰ m

Problem development

We replace data in the formula (1) to calculate q:

F=K*q₁*q₂/d²

F= K*q*q*/d²

F*d²= K*q²

F*d²/K= q²

$q=\sqrt{\frac{F*d^{2} }{K} }$

$q= d*\sqrt{\frac{F}{K} }$

$q= 3.7*10^{-10} *\sqrt{\frac{2.37*10^{-3} }{8.99*10^{9} } }$

q= 1.9*10⁻¹⁶ C