 #1
merdeka
 6
 0
 Homework Statement:

A nondeformable movable frame with square sides ##a = 30## cm has ##N = 20## spires with an electric current ##i = 5## A flowing through them. The frame is placed in a magnetic field ##\vec{B}##, with ##B = 0.4## T where the field lines make an angle ##\alpha_{i}## with the plane of the mobile frame.
What is the moment (torque) of the couples ##C_i## of the electromagnetic forces in the rotation axis ##x\prime Ox## for the four proposed values ##\alpha_i = \{0, \frac{\pi}{3}, \frac{\pi}{2}, \pi\}##?
 Relevant Equations:

##\mathbf{F} = i \boldsymbol{\ell} \times \mathbf{B}##
##F = i \ell B \sin(\alpha)##
We first determine the Laplace force for each value ##\alpha##.
$$F_{\alpha} = 5(0.3)(0.4)\sin(\alpha) = 0.6\sin(\alpha) \ \text{N}$$
We then calculate the torque at angle ##\alpha##.
$$\tau_{\alpha} = \frac{a}{2} F_{\alpha} = 2.5 F_{\alpha} \ \text{N.m}$$
Then we just plug in ##\alpha## and we should three different values (since ##\sin(0) = \sin(\pi) = 0##). But I don't understand why the numbers of spires/coils is noted here, I have the notion that the strength of the electomagnetic field is proportional to the number of coils but we haven't reached that point in class, yet. The teacher I have is very poor when it comes to correcting questions, let alone explain them. Can anyone help me understand?
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