Electromagnetism linear charge density question

[Liquidxlax]

Homework Statement

Two rods, of lengths l1 and l2, have charges q1 and q2

a)Find the charges per unit length for each rod individually.
b)Find the charge per unit length, averaged over both rods.
c)Check your result for l1 approaching 0
d)Check your result for l1=l2

Homework Equations

q = integral dq = integral lamda(ds) = lamda integral ds = lamda(l)

avg lamda equvilant to q/l equals lamda(l)/(l) = lamda (for uniform charge)

if you know ^^^ then nonuniformly charged is pretty simple to know (integral (x= 0-l) cxdx)

The Attempt at a Solution

i'm not really having trouble with this problem, its that I'm not sure how much work it requires since I'm given bare bones to work with and questions surrounding this one, had integrals and charges on spheres annulus cylinders and what have you.

If i assume it is as easy as it looks

a) lamda1 = q1/l1 and lamda2 = q2/l2

b) lamda3 = (q1+q2)/(l1+l2)

c) lamda4 = (q1+q2)/(0+l2)

d) lamda5 = (q1+q2)/(2l)

so do you think it is that simple?

 

[collinsmark]

Your attempted solution seems correct to me.

Perhaps it is a poorly worded problem (solvable yes, but just not very interesting). On the other hand, if it was worded slightly differently such as something like

...Two rods, of lengths l₁ and l₂, have charge densities λ₁ and λ₂.

...a) Find the total charge for each rod individually.
...b) Find the total charge, averaged over both rods.
...c) Check your result for l₁ approaching 0
...d) Check your result for l₁ = l₂

it would have made a more interesting problem.

 

[Liquidxlax]

Your attempted solution seems correct to me.

Perhaps it is a poorly worded problem (solvable yes, but just not very interesting). On the other hand, if it was worded slightly differently such as something like

...Two rods, of lengths l₁ and l₂, have charge densities λ₁ and λ₂.

...a) Find the total charge for each rod individually.
...b) Find the total charge, averaged over both rods.
...c) Check your result for l₁ approaching 0
...d) Check your result for l₁ = l₂

it would have made a more interesting problem.

lol, that would make it much more understandable to myself, well i talked to my prof and he said it was an easy mark. So i did the easy assumable answer