9. A circular coil of radius 10 cm and with 125 turns is initially oriented perpendicular to a uniform magnetic field of strength 2.50 mT directed out of the page. The wire carries a current of .250 A. a) Sketch the situation. b) Indicate the direction of the magnetic moment of the coil. c) What is the torque on the coil

Explanation:

Given that:

The radius = 10 cm

No of turns = 125

Current in the coil (I) = 0.250 A

Uniform magnetic field B = 2.50 mT = 2.5 × 10⁻³ T

a) The sketch of the situation can be seen below

b)The magnetic moment of the coil is

where the direction of the magnetic moment is the same and equivalent to the direction of the area vector in the diagram. The region vector of the coil is parallel to the magnetic field.

In this manner, the direction of magnetic moment is perpendicular to the current loop by right-hand rule direction; which implies out of the page.

(c)

The torque

where;

between and B = 0

Thus;

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.