A uniform circular ring of charge Q=6.30 microCoulombs and radius R=1.30cm is lo

Question

A uniform circular ring of charge Q=6.30 microCoulombs and radius R=1.30cm is located in the x-y plane, centered on the origin as shown in the figure.

1) What is the magnitude of the electric field E at point P, located at z=3.80 cm?

2) Consider other locations along the positive z-axis. At what value of z does E have its maximum value?

3) What is the maximum value of E on the z-axis?

4) 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=-kz, where k is a constant. Obtain a numerical value for k.

5) What is the frequency of the small axial oscillations that the electron will undergo if it is released along the z-axis near the origin?

Explanation / Answer

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