In an electron gun of a television set, an electron with an initial speed of 10^3 m/s enters a region where it is electrically accelerated. It emerges out of this region after 1 micro second with speed of 4 × 10^5 m/s. What is the maximum length of the electron gun.
Question
In an electron gun of a television set, an electron with an initial speed of 10^3 m/s enters a region where it is electrically accelerated. It emerges out of this region after 1 micro second with speed of 4 × 10^5 m/s. What is the maximum length of the electron gun.
Solution
To solve this problem, we need to use the equations of motion.
First, we need to find the acceleration of the electron. We can use the formula:
a = (v - u) / t
where: v = final velocity = 4 × 10^5 m/s u = initial velocity = 10^3 m/s t = time = 1 microsecond = 1 × 10^-6 seconds
Substituting these values into the formula, we get:
a = (4 × 10^5 m/s - 10^3 m/s) / 1 × 10^-6 s = 3.99 × 10^11 m/s^2
Next, we need to find the maximum length of the electron gun. We can use the formula:
s = ut + 0.5at^2
where: s = distance (which is the length of the electron gun in this case) u = initial velocity = 10^3 m/s a = acceleration = 3.99 × 10^11 m/s^2 t = time = 1 × 10^-6 seconds
Substituting these values into the formula, we get:
s = (10^3 m/s * 1 × 10^-6 s) + 0.5 * 3.99 × 10^11 m/s^2 * (1 × 10^-6 s)^2 s = 1 × 10^-3 m + 0.5 * 3.99 × 10^11 m/s^2 * 1 × 10^-12 s^2 s = 1 × 10^-3 m + 0.1995 m s = 0.2005 m
So, the maximum length of the electron gun is 0.2005 meters or 20.05 cm.
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