Calculate the acceleration of the electrons enter the plates.Which are two parallel metal plates 12 mm apart, An electric field is produced between the plates, with the top plate held at a potential of 120 V and the lower plate earthed.
To calculate the acceleration of the electrons entering the plates, we need to use the equation for the electric field and the potential difference between the plates.
The electric field (E) between the two parallel plates is given by the equation:
E = V / d
Where:
- E is the electric field in volts per meter (V/m)
- V is the potential difference between the plates in volts (V)
- d is the distance between the plates in meters (m)
In this case, the potential difference is 120 volts and the distance between the plates is 12 mm, which is equivalent to 0.012 meters.
Using the given values, we can now calculate the electric field:
E = 120 V / 0.012 m
E = 10,000 V/m
Now that we have the electric field strength, we can calculate the acceleration of the electrons using the equation for the force experienced by a charged particle in an electric field:
F = q * E
Where:
- F is the force experienced by the charged particle in Newtons (N)
- q is the charge of the particle in Coulombs (C)
- E is the electric field strength in V/m
The force experienced by an electron is given by:
F = e * E
Where:
- e is the charge of an electron, which is approximately 1.6 x 10^-19 C
Using the charge of an electron and the electric field strength we calculated, we can find the force on the electron:
F = (1.6 x 10^-19 C) * (10,000 V/m)
F = 1.6 x 10^-15 N
Finally, we can calculate the acceleration using Newton's second law, which states that Force (F) is equal to mass (m) multiplied by acceleration (a):
F = m * a
Rearranging the equation, we find:
a = F / m
The mass of an electron (m) is approximately 9.1 x 10^-31 kg.
Substituting the values, we can calculate the acceleration of the electrons:
a = (1.6 x 10^-15 N) / (9.1 x 10^-31 kg)
a = 1.76 x 10^15 m/s²
Therefore, the acceleration of the electrons entering the plates is approximately 1.76 x 10^15 meters per second squared (m/s²).