Two current-carrying wires are parallel to each other. the current in one is increased by a factor of 2 , the current in the other is increased by a factor of 3 , and the distance between the wires is decreased by a factor of 13 . what is the change in the force between the wires?

the new force is 78 times higher that the initial force before made the changes.

Explanation: In order to solve this problem we have to take into account the following expression for the force ( per length ) between currents, which is given by:

F/L=(μo*I1*I2)/(2*π*r) where μo is the magnetic permeability of vaccum and r is the distance between conductors. I1 and I2 are the currents.

Considering that I1 and I2 are increased a factor 2 and 3 , respectively,

Also considering that r is decreased by a factor of 13

The new force per Length is:

F/L=(μo*2*I1*3*I2)/(2*π*r/13) reorganising  the terms, we have

F/L=13*6 (μo*I1*I2)/(2*π*r)=78*F/L=(μo*I1*I2)/(2*π*r)=78* F/L initial

it doesn't. it was imagined up in the middle ages.

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.