The force of attraction between oppositely charged plates is a fundamental concept in electrostatics and is described by Coulomb's law. When two plates with opposite charges are placed close to each other, an electric field is created between them. This electric field exerts a force on the charges, causing them to experience an attractive force.
Coulomb's law states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. Mathematically, Coulomb's law is expressed as:
=
⋅
∣
1
⋅
2
∣
2
F=
d
2
k⋅∣q
1
⋅q
2
∣
Where:
F is the magnitude of the electrostatic force between the charges
1
q
1
and
2
q
2
.
k is Coulomb's constant, approximately equal to
8.9875
×
1
0
9
N m
2
/
C
2
8.9875×10
9
N m
2
/C
2
in SI units.
d is the distance between the charges.
In the case of oppositely charged plates, if one plate has a positive charge
q and the other has an equal magnitude but opposite (negative) charge
−
−q, and the plates are parallel and closely spaced, the electric field between them is relatively uniform.
If we consider one plate to be positively charged and the other negatively charged, the electric field lines originate from the positive plate and terminate on the negative plate. This electric field exerts an attractive force on any charged particle placed between the plates. The electric field strength (
E) between the plates is given by:
=
2
0
E=
2ϵ
0
σ
Where:
σ is the surface charge density (charge per unit area) of the plates.
0
ϵ
0
is the permittivity of free space, approximately
8.854
×
1
0
−
12
C
2
/
N m
2
8.854×10
−12
C
2
/N m
2
in SI units.
The force (
F) experienced by a point charge (
′
q
′
) placed between the plates in the electric field is given by:
=
′
⋅
F=q
′
⋅E
This force will be attractive if the point charge is opposite in sign to the charges on the plates. Keep in mind that this is a simplified explanation, and real-world situations might involve more complex geometries or distributions of charge.
Remember to use consistent units when performing calculations involving these formulas.