Solve Torque & Magnetism: Find Magnetic Field Strength

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The discussion revolves around calculating the magnetic field strength required to prevent a 10-turn wire loop from rotating in a uniform magnetic field while carrying a 2.0 A current. The participant initially attempted to balance the torques acting on the loop, noting that the magnetic field exerts force only on the segments of the wire that are perpendicular to it. After some calculations, they derived the equation B = (mg)/(20IL) and computed a magnetic field strength of 0.1225 Tesla. Ultimately, the participant realized their initial calculation was correct after a brief moment of confusion. The thread highlights the importance of careful calculation in physics problems involving torque and magnetic fields.
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Homework Statement


The 10-turn loop of wire shown in the figure lies in a horizontal plane, parallel to a uniform horizontal magnetic field, and carries a 2.0 current. The loop is free to rotate about a nonmagnetic axle through the center. A 50 mass hangs from one edge of the loop.

What magnetic field strength will prevent the loop from rotating about the axle?

Homework Equations


F = ILxB
torque = FR


The Attempt at a Solution



First I attempt to sort out the torques to see what cancels what. Since the wire loops are suppose to stay parallel to the magnetic field, the sum of the torques should be zero. Another thing to note is that the magnetic field only acts on the wire where they go perpendicular to the field. Since there are 10 loops here, that means that we have 10 times the force on each side of the wire loop (F = 10ILxB). So

mgr-10ILBr-10ILBr=0
mgr-20ILBR=0
mg=20ILB
(mg)/(20IL) = B

(.05*9.8)/(20*2*.1) = .1225 Tesla

Does this seem right?

Thanks!
 

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Never freaking mind. An hour later and nothing posted. I got it right anyway.
 
Then post what you did to get it right.

EDIT: Oh whoops. Nevermind. Your original post is 100% correct. I just screwed up my calculation.
 
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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