Here we want to study how the linear charge density changes as we change the measures of our body.
We will find that we need to add 9*Q of charge to keep the linear charge density unchanged.
I will take two assumptions:
The charge is homogeneous, so the density is constant all along the wire.
As we work with a linear charge density we work in one dimension, so the wire "has no radius"
Originally, the wire has a charge Q and a length L.
The linear charge density will be given by:
λ = Q/L
Now the length of the wire is stretched to 10 times the original length, so we have:
L' = 10*L
We want to find the value of Q' such that λ' (the linear density of the stretched wire) is still equal to λ.
Then we will have:
λ' = Q'/L' = Q'/(10*L) = λ = Q/L
Q'/(10*L) = Q/L
Q'/10 = Q
Q' = 10*Q
So the new charge must be 10 times the original charge, this means that we need to add 9*Q of charge to keep the linear charge density unchanged.
If you want to learn more, you can read:
https://brainly.com/question/14514975
