A wire loop of radius 0.37 m lies so that an external magnetic field of magnitude 0.35 T is perpendicular to the loop. The field reverses its direction, and its magnitude changes to 0.19 T in 1.3 s. Find the magnitude of the average induced emf in the loop during this time.

0.053V

Explanation:

Average induced emf is given as:

EMF(avg) = (ΔB * A)/t

Change in magnetic field strength, ΔB= 0.35 - 0.19 = 0.16T

Area, A = 3.142*r² = 3.142 * 0.37²

A = 0.43 m²

EMF(avg) = (0.16 * 0.43) / 1.3

EMF(avg) = 0.053 V

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.