Three charges -q1,+q2 and -q3 are placed as shown in figure....

Three charges $-q_{1,}+q_{2}$ and $-q_{3}$ are placed as shown in figure. The $x$ component of the force on $-q_{1}$ is proportional to (a) $\frac{q_{2}}{b^{2}}-\frac{q_{3}}{a^{2}} \sin \theta$ (b) $\frac{q_{2}}{b^{2}}-\frac{q_{3}}{a^{2}} \cos \theta$ (c) $\frac{q_{2}}{b^{2}}+\frac{q_{3}}{a^{2}} \sin \theta$ (d) $\frac{q_{2}}{b^{2}}+\frac{q_{3}}{d^{2}} \cos \theta$

Three charges $-q_{1,}+q_{2}$ and $-q_{3}$ are placed as shown in figure. The $x$ component of the force on $-q_{1}$ is proportional to
(a) $\frac{q_{2}}{b^{2}}-\frac{q_{3}}{a^{2}} \sin \theta$
(b) $\frac{q_{2}}{b^{2}}-\frac{q_{3}}{a^{2}} \cos \theta$
(c) $\frac{q_{2}}{b^{2}}+\frac{q_{3}}{a^{2}} \sin \theta$
(d) $\frac{q_{2}}{b^{2}}+\frac{q_{3}}{d^{2}} \cos \theta$

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Key Concepts

Coulomb’s Law

Coulomb’s Law is the fundamental principle for calculating the electric force between two point charges. It states that the magnitude of the force is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them, which is essential in determining how forces vary with distance in any charge configuration.

Vector Decomposition

Vector decomposition involves breaking a force into its components along the coordinate axes, typically the x and y directions. This technique is crucial when analyzing forces that act at angles, as it allows one to calculate the net force by summing the individual components derived using sine and cosine functions.

Trigonometric Functions in Force Analysis

Trigonometric functions such as sine and cosine are used to relate the angles of forces to their components in the x and y directions. When forces are not aligned along a single axis, these functions help accurately determine how much of a force contributes in each direction based on the given angle.

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