Electric field strength problem

1. Aug 4, 2008

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

Last edited: Aug 4, 2008
2. Aug 4, 2008

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?

3. Aug 4, 2008

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.)

4. Aug 4, 2008

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

5. Aug 4, 2008

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?

6. Aug 4, 2008

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.