An alpha particle travels along the z-axis with a constant speed v _z = 3.2 × 10 ⁷ m/s. Determine the magnitude and direction of the magnetic field at the point (0 cm, 5 cm, -1 cm) when the alpha particle is at (0 cm, 0 cm, -1 cm).

A conducting plate is in a 25 mT magnetic field, generating a Hall voltage of 4.5 μV. When the magnetic field is increased, keeping the current constant, a 7.8 μV voltage is measured. Calculate the new magnetic field strength.