Calculating the mass in a solenoid system

[mmoadi]

Homework Statement

Through the bigger coil with N = 10,000 turns of wire and length of L = 30 cm is flowing electric current of I = 5 A. Inside the big coil we insert a smaller coil with
N(1) = 500 turns, length of L(1) = 3 cm, and a radius r = 1 cm. The electric current flowing through the small coil is I(1) = 1 A. Axis of both coils are perpendicular to one another, smaller coil is rotatable around a rectangular axis (picture!). On the edge we attach a light string with the weight. What has to be the mass of the weight so that the small coil will not turn? In which direction do the electric currents I and I1 run?

Picture: http://item.slide.com/r/1/227/i/hpQg_yax1D-i2BRLqRDiva38H-JMSI_x/

Homework Equations

B= (μ(0)*I*N)/ L
M= p(m)*B
r(m)= I*S*N

The Attempt at a Solution

First part: What has to be the mass of the weight so that the small coil will not turn?

M= p(m)* [((μ(0)*I*N)/ L]

M= (I(1)*π*r²*N(1)* μ(0)*I*N)/ L
M(g)= m*(L(1)/2)*g

M= M(g)
(I(1)*π*r²*N(1)* μ(0)*I*N)/ L= m*(L(1)/2)*g
m= (2*I(1)*π*r²*N(1)* μ(0)*I*N)/ (g*L*L(1))
m= 2.2 kg

Are my calculations correct?

Thank you for helping!

 

[rl.bhat]

If there is no mass attached to the smaller coil, what will happen to the coil?

 

[kerimek]

I cannot verify the accuracy of your calculations without knowing the specific values for the variables. However, your approach seems correct and the equations you have used are appropriate for calculating the mass in a solenoid system. It is important to double check your units and make sure they are consistent throughout the calculation. Also, it would be helpful to provide a clear explanation of your steps and assumptions.