Four charges, each equal to -Q, are placed at the corners of a square and a charge +q is placed

step 1 Hi friends, as shown in the figure, there are four charges each of minus capital Q at the four c

Four charges, each equal to -Q, are placed at the corners of...

Four charges, each equal to $-\mathrm{Q}$, are placed at the corners of a square and a charge $+q$ is placed at its centre. If the system is in equilibrium, the value of $\mathrm{q}$ is (A) $(Q / 4)(1+2 \sqrt{2})$ (B) $-(\mathrm{Q} / 4)(1+2 \sqrt{2})$ (C) $-(Q / 2)(1+2 \sqrt{2})$ (D) $(Q / 2)(1+2 \sqrt{2})$

Four charges, each equal to $-\mathrm{Q}$, are placed at the corners of a square and a charge $+q$ is placed at its centre. If the system is in equilibrium, the value of $\mathrm{q}$ is
(A) $(Q / 4)(1+2 \sqrt{2})$
(B) $-(\mathrm{Q} / 4)(1+2 \sqrt{2})$
(C) $-(Q / 2)(1+2 \sqrt{2})$
(D) $(Q / 2)(1+2 \sqrt{2})$

Key Concepts

Equilibrium Condition

In an electrostatic system, equilibrium is achieved when the net force acting on a charge is zero. This condition is used to determine specific relationships between charges or positions in a configuration. For the system described, applying the equilibrium condition ensures that the electrostatic attractions and repulsions balance exactly, which leads to determining the appropriate value of the central charge.

Coulomb's Law

Coulomb's Law describes the electrostatic force between two point charges, stating that the magnitude of the force is proportional to the product of the charges and inversely proportional to the square of the distance between them. This law is fundamental in analyzing interactions in systems with multiple charged particles and is used to compute both the magnitude and direction of forces acting on each charge.

Superposition Principle

The superposition principle in electrostatics states that the total force or potential acting on a charge due to a collection of other charges is the vector or scalar sum of the individual forces or potentials produced by each charge. This concept is crucial when analyzing a system like a square configuration of charges, as it allows for the calculation of net forces by summing the contributions from each charge individually.

Symmetry Considerations

Symmetry plays a critical role in simplifying the analysis of charge configurations. A symmetric arrangement, such as charges placed at the corners of a square with a central charge, allows for the cancellation of forces in certain directions. Recognizing and utilizing symmetry can significantly simplify the calculation of net forces and potentials, as well as aid in understanding the behavior of the system under small perturbations.

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