Coulomb Law

In a vacuum, two point charges, $q$ and $Q$, are separated by a distance $r = 5.0$ mm. They experience an attractive force of $F = 4.0 \times 10^{-4}$ N.

Two charges, $q_1 = 1.0 \times 10^{-8}$ C and $q_2 = 2.0 \times 10^{-8}$ C, are separated by a distance $d = 1.0$ m in kerosene. A third charge, $q_3 = 3.0 \times 10^{-9}$ C, is placed on the line connecting them, at the midpoint.

In air, point charges are placed at the four corners of a square with side length $a$: $q_1=q$ (top-left), $q_2=2q$ (top-right), $q_3=-4q$ (bottom-right), and $q_4=2q$ (bottom-left). A positive unit charge ($q_0 = +1$ C) is placed at the center of the square.

An insulating charged sphere A, with charge $q_A = 2.0 \times 10^{-7}$ C, is suspended by a light spring with spring constant $k_s = 15$ N/m. When another charged sphere B is placed below A, the spring's extension increases by an additional $\Delta x = 4.0 \times 10^{-2}$ m. At this point, the distance between the spheres is $r = 0.12$ m.

A gold nucleus contains 79 protons, and an alpha particle contains 2 protons. The elementary charge is $e = 1.6 \times 10^{-19}$ C. The mass of an alpha particle is $m_{\alpha} = 6.68 \times 10^{-27}$ kg. An alpha particle is at a distance $r = 6.9 \times 10^{-15}$ m from a gold nucleus.

Two point charges, A ($q_A = +4Q$) and B ($q_B = -Q$), are separated by a distance L. A third point charge, C, is to be introduced such that all three charges are in equilibrium under electrostatic forces.

Two identical metal spheres, A and B, have charges $q_A = +Q$ and $q_B = +2Q$ and are separated by a distance $r$. The force between them is $F$. A third identical metal sphere C, with charge $q_C = -2Q$, first touches A, then touches B, and is then removed. The final distance between A and B is $r/2$.

Two identical small spheres are suspended from a common point by threads of length $L=1.0$ m. When each sphere is given a charge $q = 3.0 \times 10^{-7}$ C, they hang in equilibrium with a separation distance $d = 0.4$ m between them.

Three point charges, each with charge $-q$, are placed at the three vertices of an equilateral triangle with side length $r$. A charge $Q$ is placed at the centroid of the triangle.