Answer Happy

Need ASAP Please.
Just brief answers would be fine.
ve found the electric field on the axis of a uniformly charged circular thick ring, or annulus, with inner radius a and outer radius b is centered at the origin in the zy plane: É = 2πok²(√²+²√²+27) 2 where ke is Coulomb's constant, o is the surface charge density. Let's specifically put a negative charge Q=-1.06 x 10-18 C on the annulus, and set a = 3.59 m, and b= 14.6 m. [These numerical values won't be used until Part c)] Image size: ML Max y O (1 points) Part a Suppose we place a proton on z-axis. At which location(s) would the force on the electron be zero? Select the correct answer O At the center, where z = 0, and at infinity O The force is always zero for any position on axis O At the position z = √a² + z² - √b² +22) 2, and at infinity O At infinity only O The force is never zero for any position on axis O At the center, where z = 0 only Part b (1 points) Show that a proton displaced a small distance from the center of the thick ring will undergo simple harmonic motion by finding the linear force constant k of the effective linear restoring force on proton due to the think ring of charge: F=-kz, for a >> z [Hint: Evaluate the general force on the proton first, and then evaluate your expression in the limit that z is very small.] [Hint: Do not confuse the two "k's: ke is Coulomb's constant, and k (with no subscripts) is the linear force constant.] Select the correct answer Ο k = 2πσκ ( - ) Ok = noke Ok=nok, (-) Ok=2noke() Ok= 2nok, Ok=nokel) (1 points) Part c What is the period of the proton undergoing simple harmonic motion about center of the annulus, if Q=-1.06 x 10-18 C is the charge on the annulus, and a = 3.59 m, and b = 14.6 m? (Use Coulomb's constant k = 9 × 109 km², the mass of the proton mp = 1.7 x 10-27 kg, and the charge of the proton 9p+1.6 x 10-19 C) Select the correct answer O 1.33e-7 seconds O 2.76e-8 seconds O 4.50e-8 seconds O 7.32e-8 seconds O 4.02e-8 seconds 2a 2b X