The English Channel runs between England and France. Ocean tides cause the water in the channel to flow to the west and then, sometime later, back to the east. At the narrowest part of the Channel, the Strait of Dover, a straight-line distance of 44 km separates Dover, in England, from Calais, in France. Water flows at a maximum speed of about 1.2 m/s through the strait; it is approximately 30 m deep. At this latitude, the earth’s magnetic field is nearly vertical. We’ll assume that it is vertical, and so points directly toward the center of the earth, with magnitude 45 μT.
a. With the water flowing at its maximum speed, what is the potential difference (magnitude and sign) between Dover and Calais? (In fact, early investigators used the potential difference across a length of undersea telegraph and telephone cable to estimate the flow speed.) b. What is the magnitude of the electric field in the water due to the water's motion?

Explanation:

Potential difference is created when a long object of length l moves perpendicular to magnetic field . The potential difference created is

V = Blv where B is magnetic field , l is length and v is velocity of length l .

here V = 45 x 10⁻⁶ x 44000 x 1.2

= 2.376 volt .

b )

Electric field = V / l  ;       V is potential difference between length l .

= 2.376 / 44000

= 54 x 10⁻⁶ V/m

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.

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.