Solving a Hinged Coil's Equilibrium Angle in a Magnetic Field

AI Thread Summary
To solve for the equilibrium angle of a hinged coil in a magnetic field, the magnetic torque and gravitational torque must be balanced. The magnetic force acting on the coil is calculated using the formula torque = BIA, where B is the magnetic field strength, I is the current, and A is the area of the coil. The confusion arises in correctly decomposing the forces: the magnetic force should be associated with cos(x), while the gravitational force should be associated with sin(x). Properly analyzing these components is crucial for determining the angle at which the coil remains in equilibrium. Understanding the relationship between these forces will lead to the correct solution for the angle.
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Homework Statement


A piece of wire has a mass of .5kg and length 3m is used to make a square coil .2m on a side. The coil is hinged along the horizontal side, carries a 3.4A current, and is placed in a vertical magnetic field of magnitude 2T. Determine the angle that the plane of the coil makes with the horizontal when the coil is in equilibrium.


Homework Equations


(torque)=BIA


The Attempt at a Solution


I am having trouble decomposing the magnetic force components and the components resulting from gravity.
I keep getting cos (x) for the magnetic force and cos (x) for the gravitational force. However, the answer associates cos (x) with the magnetic field and sin(x) for the gravitational field.

Thanks for any help.
 
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This is how I am picturing the forces:
http://img100.imageshack.us/img100/1926/magnetic.png
 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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