Charge on 1cm Wire: Solve with E=Q/4πεor^2

[Zywo]

Homework Statement

The electric field 4.80 cm from a very long charged wire is ( 2100 N/C,toward the wire).
What is the charge (in nC) on a 1.0-cm-long segment of the wire?

Homework Equations

E=1/(4*pi*eo) * Q/ri^2 * cos (theta)

3. The Attempt at a Solution

I put in 9*10^9 for 1/(4*pi*eo)
I put in (.048^2+.01^2) for ri^2 and for cos theta i put .01/4.8

I thought this equation would have worked with the old plug and chug method, is this the right equation for this situation?

Thanks

 

[ideasrule]

No, that's not correct. Think about what the equation means and you'll see why.

To start off, assume that the line of charge has a charge density of lambda and use that to find an equation giving the electric field in terms of r. Then plug and chug into THAT equation.

 

[Zywo]

Ah. 2(lambda)/(4*pi*eo*r)
lambda = Q/L
Got it.
Thanks!