To derive the equation you used to solve the first part of this question what law did you use?

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The prompt asks: 'To derive the equation you used to solve the first part of this question what law did you use?'

Since the list of answer options is not provided in the data, we cannot evaluate alternative choices or compare them against Gauss's law. This means we can only discuss the reasoning for the option that is given as correct.

Option: Gauss's law. 
Gauss's law relates the electric flux through a closed surface to the enclosed charge: ∮ E · dA = Q_enclosed / ε0. This fundamental principle is often used to derive or simplify expressions for electric fields in highly symmetric situations (spherical, cylindrical, planar symmetry) because the symmetry makes the flux integral easy to evaluate. In problems where the first part involves determining an electric field or potential in a region with symmetry, Gauss's law provides a direct route to the desired relation, either by proving the field form or by linking flux to charge distribution.

Why this option can be correct in general terms. Gauss's law is a core electromagnetic principle that underpins many derived equations in electrostatics and electrodynamics. If the question’s first part required obtaining a relationship between field quantities and charge, using Gauss's law is a natural and standard approach, especially when symmetry allows the flux integral to be simplified.

Why issues might arise with missing options. Without seeing the other choices, we cannot critique alternatives such as Coulomb's law, the superposition principle, or the continuity equation, which in some contexts might also be invoked depending on the exact setup of the problem. However, with the information given, Gauss's law stands as a valid and common method for deriving key equations in electrostatics.

PHYS1221-PHYS1231-Physics 1B T1 2025

To derive the equation you used to solve the first part of this question what law did you use?

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