Final answer:
To calculate the magnetic field at a point due to a moving proton, we use the Biot-Savart Law, considering the proton's charge, velocity, distance to the point, and the magnetic constant. The magnetic field is directed along the z-axis due to the perpendicularity of the movement and observation point.
Step-by-step explanation:
To calculate the magnetic field strength at a given point due to the motion of a proton, we can use the Biot-Savart Law for a moving charge. According to this law, the magnetic field produced by a moving charge in a vacuum at a point in space is directly proportional to the charge, the velocity of the charge, and inversely proportional to the square of the distance from the charge to the point, and also depends on the angle between the velocity vector and the position vector.
Since the field is produced by a proton moving along the y-axis and we are looking for the magnetic field at a point on the x-axis (3.74 cm away from the origin), the angle between the velocity vector and the position vector is 90 degrees. At this angle, the Biot-Savart Law simplifies, and the magnetic field vector points in the z-direction. The magnitude of the magnetic field (B) at a distance r from a moving charge q with velocity v perpendicular to the line connecting the point and the charge is given by:
B = (\(\mu_0\) / (4\(\pi\))) * (q * v / r^2)
Where \(\mu_0\) is the magnetic constant (also known as the permeability of free space), which is equal to 4\(\pi\) x 10-7 T\(\cdot\)m/A. Using the charge of a proton (q = 1.6 x 10-19 C), the given velocity (v = -6.00E+6 m/s), and the given distance (r = 3.74 cm = 3.74E-2 m), we can calculate the magnetic field strength.
The resulting magnetic field strength at the point (3.74 cm, 0 cm, 0 cm) is then found by substituting the values into the equation.