- #1

Ali123

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- Homework Statement
- Hi, this is not a homework actually, I’m just kind of interested in Physic and I’m solving some more complicated problems. And with this one I’m literally lost. In school we have not been through this and the teacher wasn’t really up to any help. So I would like to ask you for help. Here is the problem:

A rectangular coil with a height a, width b, of copper wire with a diameter of d with a number of N-½ threads (or turns or loops, not sure which is the proper word) (the last thread/loop is only half) is mounted on the vertical conductive and elastic fiber (Pic. A − 4).

Pic A-4 (I'm attaching the picture)

The coil can deflect/deviates about a vertical axis given by the fiber. The coil is located in a homogeneous magnetic field with induction B in the horizontal direction. The coil is connected to a power supply with a voltage U. The current I of the coil is given by the resistance of the R resistor.

When switch S is switched off –( at rest), the plane of the coil with the direction of the magnetic field forms a zero angle α0 (α = 0). If we move the coil from the equilibrium position by a small angle α and release it, it will oscillate around the equilibrium position with the frequency f0.

After switching on the switch, the current I1 starts to go through the electrical circuit.

a) After stabilization of the coil oscillations, the new equilibrium position of the coil is given by the angle α1 of deflection from the initial position. Write the equation for the angle α1

b) After a small deflection from the new equilibrium position and release, the coil starts to oscillate with frequency f1. Determine the frequency f1 as a function of the angle α1.

c) For a given current I1, the angle α1 = fa (B) is a function of the induction B and the frequency f1 = fb (α1) is a function of the angle α1. Plot graphs of both functions for given values.

d) This way can be measured the horizontal component Bh of magnetic field induction. Determine the induction of Bh using the constructed graphs from the measured values I1 = 2.0A, f0 = 10Hz and f1 = 300Hz and the given coil parameters.

Solve the problem in general and then for values: N = 5, a = 10 cm, b = 10 cm, d = 0.20 mm, I1 = 2.0 A

- Relevant Equations
- Fm=B*I*l*sinα

f=1/T

v=s/T -->T=s/v

--> f=v/s

So my idea was that to reach the equilibrium position, the final moment of force has to be 0 (so in the end the forces will “eliminate” each other). And I found the equation Fm=B*I*l*sinα, which should characterize the force, which affects wire with the current in a magnetic field, and Fleming’s left-hand rule. But it was all about just one single wire, not the whole coil and it’s kind of difficult for me to imagine how should the rectangular coil move.

I'm attaching 2 pictures (other than the one given) because I'm not sure which way should be the coil oriented

I'm attaching 2 pictures (other than the one given) because I'm not sure which way should be the coil oriented

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