Hi there!
A)
We can use the following equation for the torque on a current-carrying loop caused by a magnetic field:
[tex]\tau = BIA[/tex]
τ = Torque (Nm)
B = Magnetic Field Strength (T)
I = Current (A)
A = Area of loop (m²)
**The torque can also be expressed as τ = μ × B. Recall the cross-product.
Plug in the given values to calculate the torque. Remember to convert cm to m.
[tex]\tau = 0.15 * 6 * (0.05 * 0.08) = \boxed{0.0036 Nm}[/tex]
B)
The Magnetic moment is equivalent to the following:
[tex]\mu = I A[/tex]
μ = Magnetic Moment (Am²)
I = Current (A)
A = Area of loop (m²)
Calculate:
[tex]\mu = 6 * (0.05 * 0.08) = \boxed{0.024 Am^2}[/tex]
C)
To find the maximum torque, we must find the maximum area that can be obtained with the same length of wire. This would be accomplished by making the loop into a circle.
We are given that the length of the wire stays the same (26 cm), so this will be the circumference of the circle.
Using the equation:
[tex]C = \pi d\\\\d = \frac{C}{\pi} \\\\d = \frac{0.26}{\pi} = 0.0828 m\\\\r = \frac{d}{2} = 0.0414 m[/tex]
Now, solve for the area of the loop.
[tex]A = \pi r^2 = \pi (0.04138^2) = 0.00538 m^2[/tex]
Using the same equation:
[tex]\tau = BIA\\\\\tau = (0.15)(6)(0.00538) = \boxed{0.00484 Nm}[/tex]
