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The magnitude of the electric field can be calculated using the equation
, where F is the Force acting on the proton and q is the charge of the proton.
We know that the charge of the proton is
We have to calculate the Force first.
We know that F = ma from Newton's 2nd law, where m is the mass of the proton and a is the acceleration.
We know that the mass of the proton
So it turns out that we have to calculate acceleration before anything else.
In order to calculate the acceleration, we make use of the following data from the question:
Initial Velocity of the proton
Distance traveled = 0.017 m
Time taken for the travel between the plates
Acceleration a = ?
Using the equation, , we get
Knowing that initial velocity is 0, the equation reduces to
Rearranging the equation so as to make a the subject of the formula, we have
Plugging in the numbers and simplifying gives us a = 1.5 x
We can now calculate the Force using F = ma
Plugging in the known values, we get F = 2.5 x
Using this, we can calculate E through the equation
Plugging the numbers and simplifying gets us E = 156.25 N/C
Thus, the magnitude of the electric field between the plates of the capacitor is 156.25 N/C
B) To calculate the Final Velocity of the proton, we can make use of the equation
Plugging the numbers in and simplifying gets us