5. Two rectilinear infinitely long conductors are located in parallel at a distance d=10 cm from each other. Currents I_(1)=I_(2)=10 A flow through the conductors in opposite directions.Find the magnitude and direction of the strength H of the magnetic field at a point located at a distance a=10 cm from each conductor.

To find the magnitude and direction of the magnetic field strength \( H \) at a point located at a distance \( a = 10 \) cm from each conductor, we can use the Biot-Savart law or Ampere's Law. However, for infinitely long straight conductors, the magnetic field at a perpendicular distance \( a \) from the conductor is given by:<br /><br />\[ H = \frac{I}{2\pi a} \]<br /><br />Since both conductors are carrying currents in opposite directions, the magnetic fields due to each conductor will add up vectorially at the point halfway between them.<br /><br />Let's calculate the magnetic field due to each conductor separately:<br /><br />For the first conductor:<br />\[ H_1 = \frac{I_1}{2\pi a} = \frac{10}{2\pi \cdot 0.1} = \frac{10}{0.2\pi} = \frac{50}{\pi} \approx 15.92 \, \text{A/m} \]<br /><br />For the second conductor:<br />\[ H_2 = \frac{I_2}{2\pi a} = \frac{10}{2\pi \cdot 0.1} = \frac{10}{0.2\pi} = \frac{50}{\pi} \approx 15.92 \, \text{A/m} \]<br /><br />Since the currents are in opposite directions, the magnetic fields at the point halfway between them will also be in opposite directions. Therefore, the net magnetic field strength \( H \) at the point located at a distance \( a = 10 \) cm from each conductor is the vector sum of \( H_1 \) and \( H_2 \):<br /><br />\[ H = H_1 + H_2 = 15.92 \, \text{A/m} + 15.92 \, \text{A/m} = 31.84 \, \text{A/m} \]<br /><br />The direction of the magnetic field will be along the axis perpendicular to the plane containing the conductors, pointing from the conductor with current \( I_1 \) towards the conductor with current \( I_2 \).<br /><br />Therefore, the magnitude of the magnetic field strength \( H \) at the point located at a distance \( a = 10 \) cm from each conductor is approximately \( 31.84 \, \text{A/m} \), and the direction is from the conductor with current \( I_1 \) towards the conductor with current \( I_2 \).