Two point charges q1=2 μc and q2=1 μc are placed at distance b=1 cm and a=2 cm from the origin

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Two point charges q1=2 μc and q2=1 μc are placed at distance...

Two point charges $q_{1}=2 \mu c$ and $q_{2}=1 \mu c$ are placed at distance $\mathrm{b}=1 \mathrm{~cm}$ and $\mathrm{a}=2 \mathrm{~cm}$ from the origin on the $\mathrm{y}$ and $\mathrm{x}$ axes as shown in figure. The electric field vector at point $\mathrm{P}(\mathrm{a}, \mathrm{b})$ will subtend an angle $\theta$ with the $\mathrm{X}$ - axis given by, (A) $\tan \theta=4$ (B) $\tan \theta=1$ (C) $\tan \theta=3$ (D) $\tan \theta=2$

Two point charges $q_{1}=2 \mu c$ and $q_{2}=1 \mu c$ are placed at distance $\mathrm{b}=1 \mathrm{~cm}$ and $\mathrm{a}=2 \mathrm{~cm}$ from the origin on the $\mathrm{y}$ and $\mathrm{x}$ axes as shown in figure. The electric field vector at point $\mathrm{P}(\mathrm{a}, \mathrm{b})$ will subtend an angle $\theta$ with the $\mathrm{X}$ - axis given by,
(A) $\tan \theta=4$
(B) $\tan \theta=1$
(C) $\tan \theta=3$
(D) $\tan \theta=2$

Key Concepts

Vector Decomposition and Trigonometric Analysis

Breaking down electric field vectors into their components along predetermined axes (usually x and y) is crucial for analyzing their spatial effects. Trigonometric relationships, such as using the arctan of the ratio of the y-component to the x-component, are then applied to determine the direction of the resultant field relative to the coordinate axes.

Superposition Principle

When multiple charges are present, the net electric field at a point is the vector sum of the individual fields from each charge. This principle allows for the separation of complex problems into simpler parts, where the fields from each charge are calculated independently and then combined.

Electric Field as a Vector Quantity

The electric field is inherently a vector, possessing both magnitude and direction. This characteristic means that when calculating the net effect from multiple charges, each individual field must be considered in terms of its directional components, requiring vector analysis.

Coulomb's Law

This fundamental principle describes how a point charge produces an electric field in the space surrounding it. The electric field’s magnitude is directly proportional to the charge’s absolute value and inversely proportional to the square of the distance from the charge. Coulomb's Law is the cornerstone for understanding electrostatic interactions.

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