The magnitude of the magnetic field created by the proton at the given position can be calculated using the formula B = μ0qv/2πr. The calculated magnitude of the magnetic field is approximately 1.92 x 10^{-6} T.
The magnitude of the magnetic field created by the proton can be calculated using the formula:
B = μ0qv/2πr
Where:
B is the magnitude of the magnetic field
μ0 is the permeability of free space (4π×10-7 Tm/A)
q is the charge of the proton (1.602 × 10-19 C)
v is the speed of the proton (750,000 m/s)
r is the distance between the proton and the point where the magnetic field is being measured (distance between (2,1) and (5,5))
Using the given values and calculating:
B = (4 × 3.14 × 10-7 × 1.602 × 10-19 C × 750,000 m/s) / (2 × 3.14 × distance)
Where distance = √((5-2)2 + (5-1)2)
distance = √((3)2 + (4)2) = √ (9 + 16) = √ 25 = 5m
Substituting back into the equation:
B = (4 × 3.14 × 10-7 × 1.602 × 10-19 C × 750,000 m/s) / (2 × 3.14 × 5)
Finally, solving the equation:
B ≈ 1.92 x 10-6 T