To solve this problem we will apply the concepts related to the Torque depending on the current (Number of turns, magnetic field and magnetic dipole moment). From these values we can find the required current value.
First at all, our values are,
[tex]r = 0.10m[/tex]
[tex]N = 10[/tex]
[tex]B = 2.0T[/tex]
[tex]\tau_{max} = 1.88N\cdot m[/tex]
The torque and a current loops is given as
[tex]\tau = NMB sin\theta[/tex]
Here,
N = Number of loops
M = Magnetic dipole moment
B = Magnetic field
the Maximum value will be given when [tex]sin\theta[/tex] is equal to 1, then
[tex]\tau_{max} = NMB[/tex]
Remember that the magnetic dipole moment is equal to the product between the current and the cross sectional area, then
[tex]\tau_{max} = NIAB[/tex]
Rearranging to find the current
[tex]I = \frac{\tau_{max}}{NAB}[/tex]
Replacing with our values we have,
[tex]I = \frac{1.88N\cdot m}{(10)(\pi (0.1m)^2)(2.0T)}[/tex]
[tex]I = 2.99 A \approx 3A[/tex]
Therefore the current must be 3A.
