Electric field (easy at least I thought so)

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The electric field strength 5.0 cm from a long charged wire is 2000 N/C, and the question is about the field strength at 10.0 cm. The initial assumption was that the field strength would decrease to 500 N/C by applying the formula E = K*q*(r head)/(r^2), but this was incorrect due to the misapplication of the formula for a line charge. The correct approach involves using Gauss's law, which accounts for the cylindrical symmetry of the electric field around a long charged wire. The discussion emphasizes the importance of understanding the geometry of the charge distribution when calculating electric fields. The confusion highlights the need to apply the appropriate formula for line charges rather than point charges.
Kalie
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The electric field strength 5.0 cm from a very long charged wire is 2000 N/C.
What is the electric field strength 10.0 cm from the wire?

Okay I thought that since the radius is double what it was before using the equation:

E= K*q*(r head)/(r^2)

I said that it decreases 1/4 and becomes 500.

Thats wrong. But obviously because I ignored r head...the vector thingy. But how do I apply it to the equation and solve for its new value?

Sigh...confused
 
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think about the symmetry... for a point charge the field is distributed in all direction (a spherical gaussian surface), for a line of charges (the lateral surface of a cylinder)... so in other words, you have used the wrong formula. Use Gauss's law to derive a new a formula (E as a fn of r)
 
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