An electron falls a distance of 4 cm in a uniform electric field of magnitude The time taken by electron in falling will be-
Question
An electron falls a distance of 4 cm in a uniform electric field of magnitude The time taken by electron in falling will be-
Solution
To find the time taken by the electron to fall in a uniform electric field, we can use the equation of motion. The equation for the distance fallen in a uniform gravitational field is given by:
d = (1/2) * g * t^2
where d is the distance fallen, g is the acceleration due to gravity, and t is the time taken.
In this case, we have an electric field instead of a gravitational field. However, we can use the same equation by replacing g with the acceleration due to the electric field, which is given by:
a = E/m
where E is the magnitude of the electric field and m is the mass of the electron.
Given that the distance fallen is 4 cm and the magnitude of the electric field is E, we can rearrange the equation to solve for t:
t = sqrt((2 * d) / a)
Substituting the values, we have:
t = sqrt((2 * 4 cm) / (E/m))
Simplifying further:
t = sqrt((8 cm) / (E/m))
t = sqrt((8 cm * m) / E)
Therefore, the time taken by the electron to fall in the uniform electric field is sqrt((8 cm * m) / E).
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