Question

Use Ampere's law for steady currents to derive the magnetic field due to a solenoid.
Four very long straight wires are closely bound together to form a small cable.
Currents carried by the wires are : I1 =15A, 12 = -10A, 13 = 20A and 14 = - 5A.
Determine B at a distance of 5 cm from the cable.

Answer 1

In accordance with Ampere's law

$$2\pi Br =\mu _0(I_1+I_2+I_3+I_4)$$

respectively

$$B=\frac{2\cdot10^{-7}(15-10+20-5)}{0.05}=8\cdot10^{-5} (T).$$