Here are the essential concepts you must grasp in order to answer the question correctly.
Electric Potential
Electric potential, denoted as V, is the amount of electric potential energy per unit charge at a point in an electric field. It is a scalar quantity that indicates the work done to move a charge from a reference point (usually at infinity) to a specific point in the field. The potential due to a point charge is given by V = k * q / r, where k is Coulomb's constant, q is the charge, and r is the distance from the charge.
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Gauss's Law
Gauss's Law relates the electric flux through a closed surface to the charge enclosed by that surface. Mathematically, it states that the total electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space (ϵ_0). This law is particularly useful for calculating electric fields in symmetric charge distributions, such as spherical shells and point charges.
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Electric Field
The electric field (E) is a vector field that represents the force experienced by a unit positive charge placed in the field. It is defined as the negative gradient of the electric potential, E = -∇V. For a point charge, the electric field decreases with the square of the distance from the charge, following the formula E = k * q / r^2. Understanding the relationship between electric field and potential is crucial for solving problems involving charge distributions.
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