The magnetic field in the solenoid is :
B = Uo*(N / L )*I
N/L = 30*100
Uo = 4*pi*10^-7
B = 4*pi*10^-7*30*100*15 = 18*pi*10^-3 (Tesla)
We have the magnetic field that is acting on the square loop of
wire.
Now, we know that the force on each side of the loop will be
:
F = I*L*B*SIN(angle)
B = 18*pi*10^-3
I = 0.15 Ampere
L = (2/100) meters
the angle is 90 degrees, because you said, that the plane fo the
loop is perpendicular to the magnetic field
so : F = 0.15*(2/100)*18*pi*10^-3 = 54*pi*10^-6 (Newtons)
This force will have the same value for each side, because it's a
square, so the have the same lenght, and also, because the magnetic
field is perpendicular to each side.
F1 = F2 = F3 = F4 = 54*pi*10^-6 (Newtons)
Now, the torque, here you need to know :
Torque = N*I*A*B*sin(angle)
B = 18*pi*10^-3 (Tesla)
sin(90) = 1, the torque acting on the loop :
0.15*(2/100)^2*18*pi*10^-3*1 = 33.93*10^-8 N.m
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