Answer :
a) The acceleration experienced by the proton due to the electric field is approximately 1.25 × 10^23 m/s^2. b) The final speed of the proton, after accelerating for 10 mm and starting from rest, is approximately 5 × 10^10 m/s.
a) To calculate the acceleration experienced by a proton due to an electric field, we can use the formula:
acceleration (a) = electric field (E) / charge of the proton (q)
The charge of a proton is 1.6 × 10^-19 C. Plugging in the given values, we have:
acceleration = (2.00 × 10^4 N/C) / (1.6 × 10^-19 C)
acceleration ≈ 1.25 × 10^23 m/s^2
b) To find the final speed of the proton, we can use the kinematic equation:
final velocity (v) = initial velocity (u) + acceleration (a) × time (t)
Since the proton starts from rest, the initial velocity (u) is 0. Given that it accelerates for a distance of 10 mm (0.01 m), we can find the time it takes using the formula:
distance (s) = (1/2) × acceleration (a) × time squared (t^2)
0.01 m = (1/2) × (1.25 × 10^23 m/s^2) × t^2
Solving for t, we find:
t^2 ≈ (0.02 m) / (1.25 × 10^23 m/s^2)
t^2 ≈ 1.6 × 10^-25 s^2
Taking the square root of both sides, we get:
t ≈ 4 × 10^-13 s
Now, we can calculate the final velocity (v):
v = 0 + (1.25 × 10^23 m/s^2) × (4 × 10^-13 s)
v ≈ 5 × 10^10 m/s
Therefore, the final speed of the proton is approximately 5 × 10^10 m/s.
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