In class your instructor derived the strength of an electric field a distance "r" from an infinitely
long, infinitely thin, uniformly charged wire whose charge per unit length was lambda .
The answer was that the electric field was given by vec(E)=(lambda )/(2pi epsi _(o)r)hat(r), where hat(r) is a unit vector that at
any point in space points away from the origin along a line from the origin to that point.
For this extra credit assignment you may choose to keep " r " and lambda as symbols or you can use r=
10.00cm and lambda =0.1113n(C)/(m) (Don't forget to pay attention to the units).
You are to assume the wire, of charge per unit length lambda , has a total length L (so that it extends
from y=-(L)/(2) to y=+(L)/(2).) and compute the electric field at a distance r from its center (really, all
you have to change
in the problem solved in class is the range of integration. They were from ylongrightarrow-infty to
ylongrightarrowinfty but now they should be from y=(-L)/(2) to y=(L)/(2) ).
Then you are to find the smallest L for which the two formulas do not differ by no more than +-
0.1% (Note: with the numbers I gave, the electric field for an infinitely long wire would be 10.00
N/C
so 0.1% would mean +-0.01(N)/(C).
Note: the 0.1%=0.001-=(E-E_(infty ))/(E), where E is the magnitude of the electric field of the finite
wire and E_(infty ) is the magnitude of the electric field due to the infinitely long wire.
In class your instructor derived the strength of an electric field a distance "r" from an infinitely Iong, infinitely thin, uniformly charged wire whose charge per unit length was .
The answer was that the electric field was given by E = 2TE0 any point in space points away from the origin along a line from the origin to that point.
For this extra credit assignment you may choose to keep "r" and A as symbols or you can use r = 10.00 cm and = 0.1113 nC/m (Don't forget to pay attention to the units) .
You are to assume the wire, of charge per unit length X, has a total length L (so that it extends
from y = -L/2 to y = +L/2.) and compute the electric field at a distance r from its center (really, al
you have to change
in the problem solved in class is the range of integration. They were from y > --oo to
Then you are to find the smallest L for which the two formulas do not differ by no more than
0.1 % (Note: with the numbers I gave, the electric field for an infinitely long wire would be 10.00 N/C
so 0.1% would mean 0.01 N/C)
Note: the 0.1% = 0.001
E
wire and Eoo is the magnitude of the electric field due to the infinitely long wire