Two parallel loops with radius R = 10 cm and current I? = 5.0A have centres at P? = (-a, 0, 0) and P? = (a, 0, 0), where a = 8.0 cm. Also, there is a straight wire with current I<sub>v</sub> = 10A that lies parallel to the x-axis through the point P? = (0, 0, D), where D = 15 cm. The current direction is shown in the figure.
a) Calculate the total magnetic field due to the current loop and the straight wire at point (0, 0, 0). Write the answer in the form:
$\vec{B} = B_x\hat{i} + B_y\hat{j} + B_z\hat{k}$.
b) For what value of D, is obtained a magnetic field at (0, 0, 0) that forms a 45° angle with the x-axis?