How Do You Incorporate Mass into the Biot-Savart Law Formula?

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AI Thread Summary
The discussion revolves around transforming the magnetic force formula derived from the Biot-Savart Law to incorporate mass. The original formula is F=(u x i2 x l)/(2 x (pi) x d), where variables represent magnetic intensity, length of conductors, and distance. The user is specifically looking to express the formula in terms of I2/m, with "m" representing mass. They provide data on the length of the string and its volumetric mass, but express uncertainty about how to proceed with the transformation. Clarification on the mathematical manipulation required for this conversion is sought.
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Homework Statement



ok i have a lab w a magnetic balance (where u have weight on one side and electrical magnetism on the other) and its using a law :

F=(u x i2 x l)/(2 x (pi) x d)

were i is intensity, l is length of hte conductors, separated by a distance d, u is 4π×10-7 kg·m·A-2·s-2

this is a derivative of biot savart law

now they are asking me to transform the formula to have I2/m (m is mass

how do i do this?

oh and my data is

1 length of string is 5cm long and has a volumic mass of 0.14567 g/m

# of 5 cm lenghts / i
1 2.48
2 4.39
3 4.92
4 5.66
5 5.88
6 6.81
7 7.41
8 7.87

Homework Equations



F=(u x i2 x l)/(2 x (pi) x d)

The Attempt at a Solution



no idea
 
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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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