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Electric Field Produced by a Ring

by smithnh
Tags: electric, field, produced, ring, solved
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smithnh
#1
Jan25-08, 12:30 PM
P: 11
1. The problem statement, all variables and given/known data

A uniform circular ring of charge Q=5.60microCoulombs and radius R=1.30 cm is located in the x-y plane, centered on the origin as shown in the figure.

If z is much smaller than R then E is proportional to z. (You should verify this by taking the limit of your expression for E for z much smaller than R.) If you place an electron on the z-axis near the origin it experiences a force Fz=-Az, where A is a constant. Obtain a numerical value for A.


2. Relevant equations

Ez= (kQz)/(R^2+z^2)^(3/2)


3. The attempt at a solution

Since R is much greater than z and the electron carries a minus sign, Ez simplifies to
(-kQz)/(R^3)

Then Eqauting Fz and Ez gives (-kQz)/(R^3)=(-)Az which then simplifies to
(kQ)/(R^3)=A

Plugging in the numbers gives (9*10^9*5.6*10^-6 C)/(.013 m)^3= 2.3*10^10 kg/s^2

What am I doing incorrectly? Any help is appreciated.
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neutrino
#2
Jan25-08, 12:54 PM
P: 2,047
Well, for one, you haven't taken into account the charge of the electron - it's magnitude to be precise. The question asks you to find the force F = qE, where q is the charge of the test particle.

Secondly, you don't have the right unit for force.
smithnh
#3
Jan25-08, 05:49 PM
P: 11
Thanks for the help.


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