Current Carrying Coil - Torque

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You already have the torque of the coil when it has the angle $\theta$, namely $\tau = NIAB \sin(\theta)$. The equilibrium will be reached when the total torque on the coil will be zero.

So look at the torque by gravity: It will pull at the center of mass, which lies $b/2$ away from the axis. Its mass is $m = 0.015 \, \mathrm{kg}$. That will give you around $F = mg = 0.15 \, \mathrm N$ of pull vertically down. The length of the lever is $b/2$, and you will have to take the angle between lever and pull into account, which is $\pi/2-\theta$. So the torque by gravity will be: $$ \tau_\text G = \frac b2 mg \sin(\pi/2-\theta)$$

Which is $$ \tau_\text G = \frac b2 mg \cos(\theta)$$

So you need to find $\theta$ so that $\tau = \tau_\text G$. I hope this is correct and I did not make any sign mistakes.

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jm22b
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Updated on March 20, 2020

Comments

  • jm22b
    jm22b over 3 years

    i'm stuck on how to answer the last part of this question and would really appreciate some pointers.

    A rectangular coil (sides $a = 15 \, \mathrm{cm}$ and $b = 20 \, \mathrm{cm}$, $m= 15 \, \mathrm{g}$), is suspended by one of its shorter sides, and lies in a vertical plane due to its weight. The coil carries a current $I = 3 \, \mathrm{A}$, directed counterclockwise. If a uniform magnetic field $B = 0.06 \, \mathrm{T}$ directed upwards is switched on, the coil rotates around the $x$ axis until it reaches a new equilibrium position (see figure). Determine:

    (a) the magnitude of the magnetic moment of the coil;

    (b) the torque acting on the coil when the coil is in a vertical position;

    (c) the angle that the coil forms with the vertical axis when the coil reaches the equilibrium position.

    a) $\mu = NIA$ (The question makes no mention of the number of coils, so I assume 1)

    $= 0.09 \, \mathrm{Am^{2}}$

    b) $\tau = NIA(B \sin \theta)$

    $\theta = 90\deg$

    $\tau = NIAB = 5.4 \cdot 10^{-3} \, \mathrm{Nm}$

    And now I'm stuck... I can picture in my head what I need to do, but I can't figure out how to apply it. I have worked out a "turning" force on the coil and I know it's length and mass, but I am unsure of how to use this info to find $\theta$.

    How do I proceed?

    Thanks!

    • Martin Ueding
      Martin Ueding over 9 years
      Please put units into \mathrm{...} as they should not be italic. Stuff like “MagneticMoment” needs to be in \text{...}. Even better, use \mu for the magnetic moment.