A10-cm-long wire is pulled along a u-shaped conducting rail in a perpendicular magnetic field. the total resistance of the wire and rail is 0.20 ω. pulling the wire at a steady speed of 4.0 m/s causes 4.0 w of power to be dissipated in the circuit. a. how big is the pulling force? b. what is the strength of the magnetic field?

In the above case we can say that power given by external agent to pull the rod must be equal to the power dissipated in the form of heat due to magnetic induction.

Part a)

when we pull the rod with constant speed then power required will be product of force and velocity

here we will have

P = 4 W

v = 4 m/s

now we will have

So external force required will be 1 N

PART B)

now in order to find magnetic field strength we can say

here we know that induced EMF in the wire is E = vBL

so power due to induced magnetic field is given by

by solving above equation we will have

this is poiselle's equation from fluid mechanic in physics. mech eng

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.