A cell membrane consists of an inner and outer wall separated by a distance of approximately 10nm. Assume that the walls act like a parallel plate capacitor, each with a charge density of 10^(−5) C/m^2, and the outer wall is positively charged. Although unrealistic, assume that the space between cell walls is filled with air.
(A) What is the magnitude of the electric field between the membranes?

a) 1×10^6 N/C
b) 1×10^15 N/C
c) 5×10^5 N/C
d) 9×10^2 N/C

(B) What is the magnitude of the force on a K+ ion between the cell walls?

a) 2×10^13 N
b) 9×10^13 N
c) 2×10^11 N
d) 3×10^12 N

(C) What is the potential difference between the cell walls?

a) 6×10^3 V
b) 1×10^7 V
c) 10 V
d) 1×10^2 V

(D) What is the direction of the electric field between the walls?

a) There is no electric field.
b) Toward the inner wall.
c) Parallel to the walls.
d) Toward the outer wall.

1) A

2) A

3) D

Explanation:

For parallel plates,the electric field E is given by:

E = σ / ε(o), where

E = Electric Field

σ = surface charge density

E = 10^-5 / 8.85*10^-12

E= 1.13*10^6 which is approximately 1*10^6 N/C, option A

B) K has a charge of 1.6*10^-19

F= q*E= (1.13*10^6) * (1.6*10^-19)

F= 1.8*10^-13 Which is approximately 2*10^-13 N, option A

C) Potential difference ,V = Ed

d = 10 nm= 1*10^-9

V = 1.13*10^6 * 1**10^-9

V = 0.0113 v

V = 1.13×10^-2 which is approximately 1x10^-2v, option D

where are the vectors ?

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.