Final answer:
The expression for the potential on the x-axis at a point f in a uniform electric field is calculated using the equation V = Ed, and for point charges, it is V = kQ/r.
Step-by-step explanation:
To find the expression for the potential v on the x-axis at a point f located at an unknown distance x, we need to know the properties of the electric field and use the appropriate physics equations. In a uniform electric field, the potential difference V is given by V = Ed, where E is the electric field strength, and d is the separation between the plates.
For an electron accelerating from a source (at position x₁ = 0) to a target at position xₒ, we can use the equation ΔV = -E(xₒ - x₁). Assuming the target is at xf = 10 cm or 0.10 m, and a given electric field E, we calculate the potential difference ΔV. If E is negative, this will ensure that the force on the electrons, F = qE, will point in the positive x-direction.
In case the charge distribution is like a point charge, we use V = kQ/r to find the voltage at a distance r from the point charge. Here, k is Coulomb's constant, Q is the charge, and r is the distance from the charge to the point of interest.