What is the frequency of the small axial oscillations that, Ask an Expert

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

What is the magnitude of the electric field E at point P, located at z= 2.40 cm?
5.942×107 N/C

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

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

If z << R then E is proportional to z. (You should verify this by taking the limit of your expression for E for z << 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.

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?

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