Final answer:
The equation V=100e ²x presents the electric potential along the x-axis, representing the voltage drop. To sketch an electric field as a function of position, one must differentiate the voltage with respect to x. Electric potential is commonly measured in volts, which are derived from the amount of work per unit charge.
Step-by-step explanation:
The equation V=100e ²x given in the question represents the electric potential along the x-axis, where V stands for voltage or potential, and x is the distance in meters. The correct representation for what the equation V=100e ²x denotes is (b) Voltage drop. To provide more clarity, electric potential is measured in volts (V), which are equivalent to Joules per Coulomb (J/C), and is named after the physicist Alessandro Volta.
To sketch a graph of the electric field E along the x-axis as a function of position x, one must understand the relationship between potential and electric field strength. The electric field strength E can be calculated as the negative gradient of the electric potential, symbolized by E = -dV/dx. For the given potential V=100e ²x, taking the derivative with respect to x provides the electric field as a function of x.
The phenomenon of the electric field in a uniform electric field can be understood better with the equation ΔUÊ = −qE (xƒ — x¡ ), revealing that the potential difference corresponds to the product of the electric field E and the distance d.