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

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The discussion revolves around calculating the charge on a 1.0-cm-long segment of a charged wire, given the electric field strength at a specific distance. The initial attempt used an incorrect formula for the electric field, leading to confusion. The correct approach involves using the charge density (lambda) to derive the electric field equation in terms of distance from the wire. The final formula provided is E = 2(lambda)/(4*pi*eo*r), where lambda represents charge per unit length. This clarification helps guide the user toward the correct method for solving the problem.
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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
 
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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.
 
Ah. 2(lambda)/(4*pi*eo*r)
lambda = Q/L
Got it.
Thanks!
 
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