In Fig. 21-27 a, particle 1 (of charge q1 ) and particle 2...

In Fig. $21-27 a$, particle 1 (of charge $q_{1}$ ) and particle 2 (of charge $q_{2}$ ) are fixed in place on an $x$ axis, $8.00 \mathrm{~cm}$ apart. Particle 3 (of charge $\left.q_{3}=+8.00 \times 10^{-19} \mathrm{C}\right)$ is to be placed on the line between particles 1 and 2 so that they produce a net electrostatic force $\vec{F}_{3, \text { net }}$ on it. Figure $21-27 b$ gives the $x$ component of that force versus the coordinate $x$ at which particle 3 is placed. The scale of the $x$ axis is set by $x_{s}=$ $8.0 \mathrm{~cm}$. What are (a) the sign of charge $q_{1}$ and (b) the ratio $q_{2} / q_{1}$ ?

Key Concepts

Coulomb's Law

Coulomb's Law describes the force of interaction between two point charges. The magnitude of the force is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them. This law is central to analyzing how individual charged particles interact from a distance and serves as the foundation for understanding forces in electrostatics.

Superposition Principle

The superposition principle states that the net force acting on a charge due to several other charges is the vector sum of the individual forces exerted by each of those charges. This concept is crucial when determining the conditions under which the forces from two or more charges cancel each other, leading to equilibrium or a specific net force outcome.

Electrostatic Equilibrium

Electrostatic equilibrium occurs when the net force on a charge is zero due to the cancellation of individual force vectors. In problems involving multiple charges, determining the position where a test charge experiences no net force involves balancing the magnitudes and directions of the forces, often requiring careful consideration of both the inverse-square law and the sign (attractive or repulsive) of the forces involved.

Charge Sign and Force Direction

The sign of a charge determines whether the electrostatic force it exerts on another charge is attractive or repulsive. Positive charges repel other positive charges and attract negative charges, while negative charges exhibit the opposite behavior. Recognizing how the sign of charges affects the direction of resulting forces is essential in predicting the overall force interactions in a system.

Graphical Analysis in Electrostatics

Graphical analysis involves interpreting plots such as force versus position graphs to understand how the net force on a charge changes with position. In electrostatics, these graphs can indicate points of equilibrium (where the force is zero) and reveal the relative strength of the contributions from different charges, which in turn can help deduce information about charge magnitudes and ratios.

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