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In: Physics

A rod of length L lies on the +x−axis with its left end at the origin....

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.

Solutions

Expert Solution

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]

genius_generous answered 1 year ago

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