Coulomb's law for the magnitude of the force F between two particles with charges Q and Q′ separated by a distance d is

|F|=K|QQ′|d2,

where K=1/4πϵ0, and ϵ0=8.854×10−12C2/(N⋅m2) is the permittivity of free space.

Consider two point charges located on the x axis: one charge, q1 = -10.0 nC , is located at x1 = -1.695 m ; the second charge, q2 = 30.5 nC , is at the origin (x=0.0000).

What is the net force exerted by these two charges on a third charge q3 = 49.5 nC placed between q1 and q2 at x3 = -1.245 m ?

Your answer may be positive or negative, depending on the direction of the force.

The net force exerted by the two charges is 10.97 x 10⁻⁵ N along negative x-direction.

Explanation:

K=1/4πϵ0, where ϵ0=8.854×10−12C2

K = 9x10⁹

The electric force on point charge q₃ due to charge q₂ is

F₃₂ = kq₃q₂ / (1.245)²

     = (9x10⁹ * 49.5x10⁻⁹ * 30.5x10⁻⁹) / (1.245)²

     = 13,587.75 x 10⁻⁹ / 1.55

     = 8.76629 x 10⁻⁵ N

The electric force on point charge q₃ due to charge q₁ is

F₃₁ = kq₃q₁ / (1.695 - 1.245)²

     = (9x10⁹ * 49.5x10⁻⁹ * 10.0x10⁻⁹) / 0.2025

     = 2.2000 x 10⁻⁵ N

The net electric force on point charge q₃ is

F₃ = -F₃₁ - F₃₂

    = - 8.76629 x 10⁻⁵ N - 2.2000 x 10⁻⁵ N

    = 10.97 x 10⁻⁵ N along negative x-direction

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.

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2