In: Physics
A rod of length L lies on the +x−axis with its left end at the origin. It has a nonuniform charge density λ = αx, where α is a positive constant. (a) What are the units of α and (b) Calculate the electric potential at a point A located at a distance d from the origin on the negative x−axis.
given :
length of rod = L
linear charge density = [x measured from origin]
a) Unit of linear charge density = C/m
unit of 'x' = m
therefore, unit of = unit of
= C/m/m = [answer]
b) see the diagram :
Consider a small element at distance x from origin of length dx.
charge on the element =
Distance of the point A from the element is (x+d).
Potential due to point charge at a distance r is given by V = kq/r
Therefore, Potential due to this element at A is -----(i)
To calculate Net potential at A due to the complete rod, we integrate the equation (i) :
[answer]