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smithnh
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[SOLVED] Electric Field Produced by a Ring
1. Homework Statement
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. Homework 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.
1. Homework Statement
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. Homework 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.