The electron gun in a television tube uses a uniform electric field to accelerate electrons from rest
to 5.0×107 m/s in a distance of 1.2 cm. What is the electric field strength?
Use F = E e = m a, and solve for the field E.
e is the electron charge and m is the electron mass. Use Coulombs and kg to get an answer for E in Volts per meter (which is the same as Newtons per Coulomb)
You will need to solve for the acceleration, a, first.
Use v = sqrt(2 a X) when solving for the acceleration.
X = 0.12 m
v = 5*10^7 m/s
2.3e12
To find the electric field strength, we can use the equation of motion for uniformly accelerated motion:
v^2 = u^2 + 2as
where:
v = final velocity of the electron = 5.0×10^7 m/s
u = initial velocity of the electron = 0 (since it starts from rest)
a = acceleration of the electron
s = distance traveled by the electron = 1.2 cm = 0.012 m
Rearranging the equation, we have:
a = (v^2 - u^2) / (2s)
Plugging in the values:
a = (5.0×10^7 m/s)^2 / (2 * 0.012 m)
a = 1.25 x 10^15 m^2/s^2
Now, we can calculate the electric field strength (E) using the equation:
E = a / q
where:
E = electric field strength
a = acceleration
q = charge of the electron = 1.6 x 10^-19 C (coulomb)
Plugging in the values:
E = (1.25 x 10^15 m^2/s^2) / (1.6 x 10^-19 C)
E = 7.81 x 10^33 N/C
Therefore, the electric field strength is approximately 7.81 x 10^33 N/C.
To find the electric field strength, we can use the equation for the acceleration of an object in a uniform electric field:
a = qE/m
Where:
- a is the acceleration of the electron
- q is the charge of the electron
- E is the electric field strength
- m is the mass of the electron
First, let's determine the charge and mass of the electron:
The charge of an electron is approximately -1.6 x 10^-19 Coulombs.
The mass of an electron is approximately 9.1 x 10^-31 kilograms.
Next, we can rearrange the equation to solve for the electric field strength (E):
E = (m x a) / q
We have the acceleration (a) = (final velocity - initial velocity) / time.
Given:
- Initial velocity (u) = 0 (since the electrons start from rest)
- Final velocity (v) = 5.0 x 10^7 m/s
- Distance (s) = 1.2 cm = 0.012 m
We can calculate the time (t) using the formula: t = s / v.
Substitute the values into the equation and solve for t.
t = 0.012 m / 5.0 x 10^7 m/s
Now that we have the time, we can calculate the acceleration (a) using the formula.
a = (v - u) / t
Substitute the values into the equation and solve for a.
Once we have the acceleration (a), we can substitute it, along with the charge (q) and mass (m) of the electron, into the equation for the electric field strength (E) to find the answer.