If we have I= 7.5 A:
I think my solution might just help you answer the problem on your own:
You have the formulas correct, watch your signs and BRACKETS.
B = μ0/(2π) (Current) / (Perpendicular distance)
Since μ0=4π E -7 Tm/A, we have:
B1 = (4πE-7 Tm/A)(7.5 A)/[2π (0.030 m)] = 5E-5 T
B2 = (4πE-7 Tm/A)(-7.5 A)/[2π (0.150 m)] = -1E-1 T
So BA = B1 + B2 = ?
(It looks like you just left out the square brackets, hence multiplying Pi and 0.03 and 0.15 instead of dividing them.)
<span>For the point B, the two distances are -0.060 m and +0.060 m. Be careful with the signs. Unlike point A, the two components will have the same sign.</span>
The heat needed is given by Mcθ , where m is the mass in Kg, c is the heat capacity of aluminium, and θ is the change in temperature.
Specific heat capacity of aluminium is 0.9 j/g°c
thus; Heat = 55 × 0.9 × 72.2
= 3573.9 Joules or 3.574 kJ
