an electron moves a distance of 6.0 cm when accelerated from rest by an electric field of strength 2*10^4 n/c . Calculate the time of travel?
To calculate the time of travel for an electron accelerated by an electric field, we can use the equation:
\(d = \frac{1}{2}at^2\)
where
- d is the distance traveled by the electron,
- a is the acceleration experienced by the electron, and
- t is the time of travel.
Given that the distance traveled by the electron is 6.0 cm and the acceleration is caused by an electric field of strength 2 * 10^4 N/C, we can substitute these values into the equation:
\(6.0 = \frac{1}{2} \times (2 \times 10^4) \times t^2\)
Simplifying the equation:
\(6.0 = 10^4 \times t^2\)
Rearranging the equation to solve for t:
\(t^2 = \frac{6.0}{10^4} = 6.0 \times 10^{-4}\)
Now, we can take the square root of both sides of the equation:
\(t = \sqrt{6.0 \times 10^{-4}}\)
Calculating the value:
\(t \approx 2.44 \times 10^{-2}\) s
Therefore, the time of travel for the electron is approximately 2.44 x 10^-2 seconds.
To calculate the time of travel, we can use the equation of motion for uniformly accelerated motion:
s = ut + (1/2)at^2
Where:
s = distance traveled (6.0 cm or 0.06 m)
u = initial velocity (0 m/s since the electron starts from rest)
a = acceleration (given as the electric field strength, 2*10^4 N/C)
t = time of travel (what we need to find)
Rearranging the equation, we get:
t^2 = (2s/a)
t = sqrt(2s/a)
Substituting the given values, we have:
t = sqrt(2 * 0.06 m / (2 * 10^4 N/C))
Simplifying further:
t = sqrt(0.03 / 10^4)
t = sqrt(3 * 10^-6)
t = sqrt(3) * 10^-3
Therefore, the time of travel is approximately 0.0173 ms or 1.73 * 10^-5 s.
Force=Eq
d=1/2 a t^2
t=2*d/a but a= Force/mass
time= 2*d*m/Eq
so put in the mass, and charge on the electron, and you have it.