The ratio of the magnitude of 2 to the magnitude of 1 is 1.
How solve the problem?
To solve this problem, we can use the concept of electric field and kinematics.
We know that the force acting on a proton due to an electric field is given by the equation F = qE, where q is the charge of the proton and E is the electric field.
Since the proton is released from rest, we can assume that the initial velocity of the proton is zero.
Using kinematic equations, we can find the final velocity of the proton after it has been in electric field 1 for 29.8 seconds.
v = at = Eq/m * t = Eq* t / m
where a is the acceleration of the proton due to the electric field, t is the time it spends in the field, m is the mass of the proton,
Now we can use the final velocity to calculate the distance traveled by the proton in field 1.
s = vit + 0.5at^2 = Eq* t^2 / 2m
Once the proton is in field 2, it will have a velocity in the opposite direction, and it will be acted upon by the new electric field 2, which will cause it to decelerate and eventually come to rest again.
vf = vi + at = -Eq* t / m
Now we can calculate the time it takes for the proton to come to rest again
s = vit + 0.5at^2 = Eq* t^2 / 2m
where s is the distance traveled by proton in field 2, vf is the final velocity of the proton, and vi is the initial velocity of the proton.
Now we can equate the distance traveled in field 1 and field 2 to the distance traveled in 7.65 sec.
Eq1* t^2 / 2m = Eq2* t^2 / 2m
Eq1/Eq2 = 1
So the ratio of the magnitude of 2 to the magnitude of 1 is 1