Final answer:
The time it takes for the radiative electric field to reach the detector can be calculated using the position vector and equations of motion. The direction of the radiative electric field observed at the detector location depends on the charge of the accelerating particle. If the particle had been an electron instead of a proton, the direction of the radiative electric field would be reversed.
Step-by-step explanation:
In order to calculate the time it takes for the radiative electric field to reach the detector located at <0.2, 0, 0> m, we need to determine the velocity of the proton when it reaches that position. Since the proton is only accelerated in the -y direction, its velocity in the -y direction will increase over time. We can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Since the proton is initially at rest and only accelerated in the -y direction, the initial velocity (u) is 0. Using the given position vector <0.2, 0, 0> m, we can calculate the time (t) it takes for the proton to reach that position.
The direction of the radiative electric field observed at the detector location depends on the charge of the accelerating particle. Since the particle in this case is a proton, which has a positive charge, the radiative electric field would be directed away from the proton, in the opposite direction of its acceleration. So, for this location, the direction of the radiative electric field observed would be in the positive y direction.
If the accelerated particle had been an electron instead of a proton, its charge would be negative. Therefore, the direction of the radiative electric field observed at the same location would be in the opposite direction of the proton, which is the -y direction.