Two large, parallel, conducting plates are 20 cm apart and have charges of equal magnitude and opposite sign on their facing surfaces. An electrostatic force of 3.0 10-15 N acts on an electron placed anywhere between the two plates. (Neglect fringing.)
a) Find the magnitude of the electric field at the position of the electron.
b) What is the potential difference between the plates?
F=qE=eE =>
E=F/e=3•10⁻¹⁵/1.6•10⁻¹⁹= 1.875•10⁴ N
E=Δφ/Δx= Δφ/d =>
Δφ=Ed=1.875•10⁴•0.2=3.75•10³ V
Consider
To find the magnitude of the electric field at the position of the electron (question a), we can use Coulomb's Law. Coulomb's Law states that the electrostatic force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Step 1: Determine the magnitude of the charge on the electron.
The problem states that the electrostatic force is acting on an electron. The charge of an electron is -1.6 x 10^-19 Coulombs (C).
Step 2: Determine the distance between the plates.
The problem states that the parallel plates are 20 cm apart. We need to convert this to meters, so the distance between the plates is 0.2 meters (m).
Step 3: Calculate the magnitude of the electric field (E) using Coulomb's Law.
Coulomb's Law equation is given by:
Electrostatic force (F) = (Charge 1 x Charge 2) / (4πε₀r²)
Where:
F = Electrostatic force acting on the electron (3.0 x 10^-15 N)
Charge 1 = Charge of the electron (-1.6 x 10^-19 C)
Charge 2 = Charge on the plates (which is not specified but can be assumed to be positive)
ε₀ = Permittivity of free space (8.85 x 10^-12 C²/N m²)
r = Distance between the plates (0.2 m)
Rearranging the equation for electric field (E):
E = F / (Charge 1 x (4πε₀r²))
Substituting the given values:
E = (3.0 x 10^-15 N) / (1.6 x 10^-19 C x (4π x 8.85 x 10^-12 C²/N m² x (0.2 m)²))
Calculating this expression will give us the magnitude of the electric field at the position of the electron (a).
To find the potential difference between the plates (question b), we can use the formula relating electric field and potential difference.
Potential difference (V) = Electric field (E) x Distance (d)
Where:
V = Potential difference between the plates (what we need to calculate)
E = Electric field (calculated in part a)
d = Distance between the plates (0.2 m)
By substituting the known values, we can calculate the potential difference between the plates (b).