Answer:
F= σ² L² /2ε₀
F = (L² ε₀/4π) ΔV² / r⁴
Explanation:
a) For this exercise we can use Coulomb's law
F = - k Q² / r²
where the negative sign indicates that the force is attractive and the value of the charge is equal to the two plates
Capacitance is defined by
C = Q / ΔV
Q = C ΔV
also the capacitance for a parallel plate capacitor is related to its shape
C = ε₀ A / r
we substitute
Q = ε₀ A ΔV / r
we substitute in the force equation
F = k (ε₀ A ΔV / r)² / r²
k = 1 / 4πε₀
F = ε₀ /4π L² ΔV² / r⁴4
F = L² ΔV² ε₀/ (4π r⁴)
F = (L² ε₀/4π) ΔV² / r⁴
b) Another way to solve the exercise is to use the relationship between the force and the electric field
F = q E
where we can calculate the field created by a plane using Gaussian law, where we use a cylinder with a base parallel to the plate as the Gaussian surface
Ф = ∫E .dA =
/ ε₀
the plate have two side
2E A = q_{int} / ε₀
E = σ / 2ε₀
σ = q_{int} / A
substituting in force
F = q σ / 2ε₀
the charge total on the other plate is
q = σ A
q = σ L²
F= σ² L² /2ε₀
Answer:
0.018 J
Explanation:
The work done to bring the charge from infinity to point P is equal to the change in electric potential energy of the charge - so it is given by

where
is the magnitude of the charge
is the potential difference between point P and infinity
Substituting into the equation, we find

Answer:
- 3 meter
Explanation:
A dog has started motion from +3 meter. ...(Given)
∴ maximum positive distance = + 3 meter
Magnitude of distance = 3
Maximum negative distance = (-) (magnitude of distance)
Maximum negative distance = (-) (3)
Maximum negative distance = -3 meter
Hence, maximum negative distance is -3 meter.
Answer:
P=740 KPa
Δ=7.4 mm
Explanation:
Given that
Diameter of plunger,d=30 mm
Diameter of sleeve ,D=32 mm
Length .L=50 mm
E= 5 MPa
n=0.45
As we know that
Lateral strain



We know that




So the axial pressure


P=740 KPa
The movement in the sleeve


Δ=7.4 mm
An oven mitt is used to take the tray out of the oven because it’s an insulator.