Three straight and long wire form the equilateral triangle of the figure without touching themselves. The circle in the triangle has center and radius r = 10 cm. The currents in conductors have the directions indicated in the figure, and are equal to i₁ = i₂ = 10 A and i₃ = 5 A. Determine the resultant magnetic field vector in C   \( \left(\mu_{0}=4\pi \times 10^{-7}\;\frac{\text{T.m}}{\text{A}}\right) \).

In the figure, we have three conductors, A, B, and C, parallels. In the wires flow the currents i_A=10 A, i_B=20 A and i_C=30 A, in the indicated directions, at a distance of \( L=2\sqrt{3\;}\ \text{m} \) from each other. Determine the vector of the magnetic field in the center O of the triangle (centroid). Assume \( \mu_{0}=4\pi \times 10^{-7}\frac{\text{T.m}}{\text{A}} \).

Two circular loops E₁ and E₂, concentric and coplanar with radii R₁=10π cm e R₂=2,5π cm carry currents i₁ e i₂, shown in the figure. The current i₁ = 10 A and \( \mu_{0}=4\pi \times10^{-7}\;\frac{\text{T.m}}{\text{A}} \).
a) Calculate the vector of the magnetic field created by the current i₁ in the center O; b) Determine the current i₂ so that the resultant magnetic field in the center will be zero.

Two equal circular loops E₁ and E₂, placed in perpendicular planes with coincident centers and radii R=5 π cm, carry currents i₁=3 A e i₂=4 A, as indicated in the figure. Assume \( \mu_{0}=4\pi \times 10^{-7}\,\frac{\text{T.m}}{\text{A}} \). Determine the vector of themagnetic field in the center O.

In the figure, the battery maintains a solenoid current with resistance R = 9 Ω. The solenoid has ten turns per centimeter. Assume   \( \mu_{0}=4\pi\times 10^{-7}\;\frac{\mathrm{T.m}}{\mathrm{A}} \).
a) Determine the magnitude of the magnetic field vector inside the solenoid;
b) Is the X end of the solenoid a North pole or a South pole?

A compass is placed inside an XY horizontal axis solenoid. The horizontal component of the earth's magnetic field is B_h and the solenoid has N turns of length ℓ. The solenoid axis is arranged perpendicular to the direction of the compass needle. Calculate the angle α described by the needle when the solenoid is traversed by a current of intensity i in the direction shown in the figure.