A uniformly charged thin ring has radius 15.0 cm and total charge 20.0 nC . An electron is placed on the ring's axis a distance 30.0 cm from the center of the ring and is constrained to stay on the axis of the ring. The electron is then released from rest. Required:
a. Describe the subsequent motion of the electron.
b. Find the speed of the electron when it reaches the center of the ring.

The membrane surrounding a living cell consists of an inner and an outer wall that are separated by a small space. assume that the membrane acts like a parallel plate capacitor in which the effective charge density on the inner and outer walls has a magnitude of 7.0 × 10-6 c/m2. (a) what is the magnitude of the electric field within the cell membrane? (b) find the magnitude of the electric force that would be exerted on a potassium ion (k+; charge = +e) placed inside the membrane.

Aparticle moves in the xy plane with constant acceleration. at time zero, the particle is at x = 6 m, y = 8.5 m, and has velocity ~vo = (9 m/s) ˆı + (−2.5 m/s) ˆ . the acceleration is given by ~a = (4.5 m/s 2 ) ˆı + (3 m/s 2 ) ˆ . what is the x component of velocity after 3.5 s? answer in units of m/s.

Ethanol has a heat of vaporization of 38.56 kj/mol and a normal boiling point of 78.4 c. what is the vapor pressure of ethanol at 14 c?