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Answer:
1) The total charge of the top plate is 0.008 C
b) The total charge of the bottom plate is -0.008 C
2) The electric field at the point exactly midway between the plates is 0
3) The electric field between plates is approximately 1.1294 × 10¹² N/C
4) The force on an electron in the middle of the two plates is approximately 1.807 × 10⁻⁷ N
Explanation:
The given parameters of the parallel plate capacitor are;
The dimensions of the plates = 4 × 2 cm
The distance between the plates = 10 cm
The surface charge density of the top plate, σ₁ = 10 C/m²
The surface charge density of the bottom plate, σ₂ = -10 C/m²
The surface area, A = 0.04 m × 0.02 m = 0.0008 m²
1) The total charge of the top plate, Q = σ₁ × A = 0.0008 m² × 10 C/m² = 0.008 C
b) The total charge of the bottom plate, Q = σ₂ × A = 0.0008 m² × -10 C/m² = -0.008 C
2) The electrical field at the point exactly midway between the plates is given as follows;
Therefore, we have;
The distance to the midpoint between the two plates = 10 cm/2 = 5 cm = 0.05 m
The electric field at the point exactly midway between the plates, = 0
3) The electric field, 'E', between plates is given as follows;
E ≈ 1.1294 × 10¹² N/C
The electric field between plates, E ≈ 1.1294 × 10¹² N/C
4) The force on an electron in the middle of the two plates
The charge on an electron, e = -1.6 × 10⁻¹⁹ C
The force on an electron in the middle of the two plates, = E × e
∴ = 1.1294 × 10¹² N/C × -1.6 × 10⁻¹⁹ C ≈ 1.807 × 10⁻⁷ N
The force on an electron in the middle of the two plates, ≈ 1.807 × 10⁻⁷ N
Answer:
1. the electric potential energy of the electron when it is at the midpoint is - 2.9 x J
2. the electric potential energy of the electron when it is 10.0 cm from the 3.00 nC charge is - 5.04 x J
Explanation:
given information:
= 3 nC = 3 x
C
= 2 nC = 2 x
C
r = 50 cm = 0.5 m
the electric potential energy of the electron when it is at the midpoint
potential energy of the charge, F
F = k
where
k = constant (8.99 x )
electron charge, = - 1.6 x
C
since it is measured at the midpoint,
r =
= 0.25 m
thus,
F =
= k + k
= (
)
= (8.99 x )( - 1.6 x
)(3 x
+2 x
)/0.25
= - 2.9 x J
the electric potential energy of the electron when it is 10.0 cm from the 3.00 nC charge
= 10 cm = 0.1 m
= 0.5 - 0.1 = 0.4 m
F = k + k
= (
+
)
= (8.99 x )( - 1.6 x
)(3 x
/0.1+2 x
/0.4)
= - 5.04 x J