# Calculating the mass in a solenoid system

1. Jan 15, 2010

1. The problem statement, all variables and given/known data

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/ [Broken]

2. Relevant equations

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

3. 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!

Last edited by a moderator: May 4, 2017
2. Jan 15, 2010

### rl.bhat

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