Electric Charge and Electric Force Practice Test

Electric charge is a conserved property of matter measured in coulombs (C); it comes in positive and negative types, and the total charge of an isolated system remains constant. Electric forces act at a distance: like charges repel, unlike charges attract, and the force magnitude depends on charge and separation. In space, two point charges $q_1=+4.0\times10^{-6}\ \text{C}$ and $q_2=+1.0\times10^{-6}\ \text{C}$ are fixed $0.30\ \text{m}$ apart. Coulomb’s Law gives the magnitude: $F=k\frac{|q_1q_2|}{r^2}$. A numerical check: $$F=(8.99\times10^{9})\frac{(4.0\times10^{-6})(1.0\times10^{-6})}{(0.30)^2}$$. If a third charge is later introduced, the principle of superposition states the net force on any charge equals the vector sum of forces from each other charge calculated separately.

How does the force between charges change if the distance is doubled?

Electric charge is a conserved property of matter (C) that can be positive or negative; forces between charges are electric forces that act along the line joining charges. In deep space, three point charges lie on the x-axis: $q_1=+1.0\times10^{-6}\ \text{C}$ at $x=0$, $q_2=+1.0\times10^{-6}\ \text{C}$ at $x=0.20\ \text{m}$, and $q_3=-2.0\times10^{-6}\ \text{C}$ at $x=0.40\ \text{m}$. Coulomb’s Law gives each pairwise force magnitude, e.g. $$F_{21}=k\frac{|q_2q_1|}{(0.20)^2},\quad F_{23}=k\frac{|q_2q_3|}{(0.20)^2}$$ with $k=8.99\times10^{9}$. By superposition, the net force on $q_2$ is the vector sum of forces from $q_1$ and $q_3$.

Determine the net electric force on $q_2$ placed in an electric field.