(a) Calculate the magnitude and direction (relative to the +...

(a) Calculate the magnitude and direction (relative to the $+ x$-axis) of the electric field in Example 21.6. (b) A $-$2.5-nC point charge is placed at point $P$ in Fig. 21.19. Find the magnitude and direction of (i) the force that the $-$8.0-nC charge at the origin exerts on this charge and (ii) the force that this charge exerts on the $-$8.0-nC charge at the origin.

Key Concepts

Newton’s Third Law (Action-Reaction Principle)

Newton’s third law states that for every action, there is an equal and opposite reaction. In the context of electrostatics, when one charge exerts a force on another, the second charge exerts an equal and opposite force on the first, emphasizing the mutual interactions between charged particles.

Vector Addition in Electrostatics

Because both electric fields and forces are vector quantities, their complete description requires consideration of both magnitude and direction. This involves decomposing the vectors into components (typically along the x and y axes) and then summing these components to determine the net vector.

Coulomb’s Law

Coulomb’s law quantifies the electric force between two point charges, stating that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law provides the foundational relationship for analyzing forces and fields in electrostatics.

Electric Force

Electric force is the interaction between charged particles, and its magnitude is given by Coulomb’s law. It is a vector quantity, implying that both its magnitude and direction are important in determining how charges interact in a system.

Electric Field

The electric field is a vector field representing the force per unit charge experienced by a small positive test charge placed in the vicinity of other electric charges. Its magnitude is calculated as the force divided by the charge and its direction is the direction of the force a positive test charge would experience.

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