An electron is released from rest at the negative plate of a parallel plate capacitor. The charge per unit area on each plate is σ = 1.67 10-7 C/m2, and the plate separation is 1.35 10-2 m. How fast is the electron moving just before it reaches the positive plate?
Answer in m/s
To find the speed of the electron just before it reaches the positive plate of a parallel plate capacitor, we can use the principle of conservation of energy.
First, we need to find the electric potential energy gained by the electron as it moves from the negative plate to the positive plate. The formula for electric potential energy is given by:
PE = qV
Where:
PE is the electric potential energy
q is the charge of the electron
V is the potential difference between the plates
The charge per unit area on each plate, σ, can be expressed in terms of charge per unit area:
σ = q/A
Where:
σ is the charge per unit area
q is the charge of the electron
A is the area of the capacitor plates
The area of the plates can be determined from the plate separation and the dimensions of the capacitor:
A = (length) * (width)
Now, to find the potential difference, V, between the plates, we can use the formula:
V = Ed
Where:
V is the potential difference
E is the electric field between the plates
d is the plate separation
The electric field, E, can be calculated using the formula:
E = σ / ε0
Where:
E is the electric field
σ is the charge per unit area
ε0 is the permittivity of free space (8.85 × 10^-12 C^2/N*m^2)
Finally, we can substitute the expressions for A, V, and E into the equation for electric potential energy and solve for the speed of the electron.
Kinetic energy (KE) can be equated to the potential energy (PE) to find the speed (v) of the electron using the formula:
KE = (1/2) * mv^2
Where:
KE is the kinetic energy
m is the mass of the electron (9.11 × 10^-31 kg)
v is the speed of the electron
Setting KE equal to PE, we can solve for v. I will now perform the necessary calculations to find the speed of the electron just before it reaches the positive plate.