Plate Capacitor
What is the charge Q on the positive plate of the capacitor?
A parallel-plate capacitor with plates of area 420 cm2 is charged to a potential difference V and is then disconnected from the voltage source. When the plates are moved 0.3 cm farther apart, the voltage between the plates increases by 100 V.
(a) What is the charge Q on the positive plate of the capacitor?
(b) How much does the energy stored in the capacitor increase due to the movement of the plates?
ε₀=8.854e-12 C²N⁻¹m⁻²
S=0.042 m²
Δd=0.003 m
ΔU=100 V
d=initial distance between the plates
U=initial voltage between the plates
Q=charge on the positive plate
(a) C=ε₀S/d is the initial capacitance of the parallel-plate capacitor
C1=ε₀S/(d+Δd) is the capacitance after moving the plates
U=Q/C
U+ΔU=Q/C1 is the voltage after moving the plates ==>
Qd/(ε₀S)+ΔU=Q(d+Δd)/(ε₀S) ==>
ΔU=Q*Δd/(ε₀S)
Q=ε₀S*ΔU/Δd
Q=8.854e-12*0.042*100/0.003=12.4e-9 C
(b) W=0.5QU initial energy
W1=0.5Q(U+ΔU)
ΔW=W1-W=0.5Q*ΔU=0.5*12.2e-9*100
ΔW=0.62e-6 J
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