Electric field strength of wire problem

[jwoo]

The electric field strength 5 cm from a very long charged wire is 2000N/C . What is the field strength 10 cm from wire.
A)1x10^-4 N/C
B)1x10^3 N/C
C)9.9x10^7 N/C
D) None of these

I have
E=kq/r^2 and infinite line charge E=(2k\lambda)/R

2000 * .05 m^2 /K =q
q=5.56 E-8
k5.56E-8/.^21 m = 500 N/C so my answer would be D

But its wrong so where am I off? Thanks for the help

 

[Dick]

The field from a line charge and the field from a point charge have completely different forms. Don't mix them. Why don't you solve for lambda instead of q?

 

[G01]

You have an infinite line of charge, so use that formula. The formula you are using is for point charges, not lines of charge.

(Edit: Dick beat me to it.)

 

[jwoo]

okay so
E = k2lambda/r
(2000*.05)/2k =5.56x10^-9 = lambda
plug this in
5.56x10^-9 * k * 2 / .1 = E = 9.8x10^4 still not any of the answers

 

[Dick]

Put units on numbers, ok? I get 999.41 V/m. The difference between that and one of your numbers is pure round off. BTW, you didn't even have to solve for lambda. You are trying to compare 2*k*lambda/(0.05m)=2000 V/m with 2*k*lambda/(0.1m). Everything else is the same, but the denominator doubled. What's the exact answer?

 

[jwoo]

Oh okay I see it. sorry I converted everything to meters. So then my answer would be the same as yours 999.99 which would be 1 x 10^3 . Thank you guys so much. I was having trouble with this because the logic just didnt make any sense. I gather I could've conceptually answered the problem but I wanted to know the math behind it. Thanks again.