Question

UN uniform ombs and ane, center A uniform circular ring of charge Q= 4.30 microCoulombs and radius R= 1.10 cm is located in the x-y plane, centered on the origin as shown in the figure. What is the magnitude of the electric field E at point P, located at z= 3.90 cm? Submit Answer Tries 0/40 Consider other locations along the positive z-axis. At what value of z does E have its maximum value? Submit Answer Tries 0/40 What is the maximum value of E on the z-axis? Submit Answer Tries 0/40 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. Submit Answer Tries 0/40 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? Submit Answer Tries 040.

Answer 1

a) Magnitude of the electric field, E at point P located at z=3.90 cm

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

= (9 * 10^9 * 4.30 * 10^-6 *3.90 * 10^-2 ) / [sqrt((3.90cm^2 + 1.10cm ^2))^3]

= 2.27 * 10^7 N/C

b) z = R/sqtr(2)

= (1.10 cm) / (sqrt 2)

= 0.778 cm

= 7.78*10^-3 m

c) z = 7.78 * 10^-3 m

E = kQz / sqrt(z^2 + R^2)^3

= (9 * 10^9 * 4.30 * 10^-6 *7.78 * 10^-3 ) / [sqrt((0.778cm^2 + 1.10cm ^2))^3]

= 1.23 * 10^8 N/C

d) K = eKQ / R^3

e = 1.6x10 -19

k = (1.6 * 10^-19 * 9* 10^9 * 4.30* 10-6) / (1.10cm)^3

= 4.65 * 10-9 N/m