A positive charge q is fixed at the point x = 0, y = 0, and a negative charge -2
ID: 3279303 • Letter: A
Question
A positive charge q is fixed at the point x = 0, y = 0, and a negative charge -2q is fixed at the point x = a, y = 0. Derive an expression for the potential V at points on the x-axis as a function of the coordinate x. Take V to be zero at an infinite distance from the charges. Express your answer in terms of the given quantities and appropriate constants. V(x) = ____ At which positions on the x-axis is V = 0? Express your answer in terms of a. x = ______ What does the answer to part A become when x > > a? Express your answer in terms of the variables q, a, and the Coulomb constant k. V = _____ Explain why this result is obtained. Essay answers are limited to about 500 words (3800 characters maximum, including spaces).Explanation / Answer
A positive charge 'q' is fixed at the point x= 0, y= 0, and a negative charge '-2q' is fixed at the point x=a , y = 0.
a) The electric potential V is a scalar
Suppose P is a point at distance x from +q on the x axis
The electric potential at distance x from+q =V1= kq / x
The electric potential at distance (x-a) from - 2q =V2= -2kq / (x - a)
Total electric potential =V1 + V2
Total electric potential = kq / x -2kq / (x - a)
Total electric potential =kq { (1 / x) - [2 / (x - a)] }
Total electric potential =kq ( x -a -2x) / x (x - a)
Total electric potential =kq ( x + a) / x (a - x)
= (1/4pi eo)[1/x -2/(x-a)
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