A rectangular loop (area = 0.250 m 2) turns in a uniform magnetic field with B = 0.210 T. At an instant when the angle between the magnetic field and the normal to the plane of the loop is π/2 rads and increasing at the rate of 0.530 rad/s, what is the magnitude of the emf induced in the loop?

0.0525 V

Explanation:

Given,

area of the loop, A = 0.250 m²

Magnetic field, B = 0.210 T

θ= 90°

angular speed,ω = 0.530 rad/s

Using emf expression

E = NBAω sin θ

E = 1 x 0.250 x 0.210 x sin 90°

E = 0.0525 V

The emf induced in the loop is equal to 0.0525 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.