Dimensions of Parallel Plate Capacitors

AI Thread Summary
The discussion revolves around calculating the dimensions of parallel plate capacitors given a changing electric field and displacement current. The relevant equations include the relationship between displacement current, electric field change, and capacitance. The user initially struggled with the problem but eventually derived the area of the plates as approximately 6.03 x 10^-4 m², leading to a radius of about 1.4 cm. However, it was noted that the gap distance between the plates cannot be determined without additional information about the voltage change rate. The conversation emphasizes the importance of understanding the relationships between electric field, displacement current, and capacitance in capacitor calculations.
David Truong
Messages
9
Reaction score
0

Homework Statement


The electric field between two circular plates of a capacitor is changing at a rate of 1.5 x 10^6 V/m per second. If the displacement current at this instant is Id = 0.80 x 10^-8A, find the dimensions of the plate.

Homework Equations



Id = ΔQ/Δt = ε0(ΔΦE/Δt)
ΦE = EA
Q = CV
C = ε0AE
ε0 = 8.85 x 10^-12

The Attempt at a Solution



I am unsure how to go about this question. Any guidance is appreciated!
 
Physics news on Phys.org
You're told Id and ΔE/Δt ... I'm pretty sure you can look up ε in the textbook front cover. So, how does A depend on radius?
(btw, your Capacitance equation should be εA/d, where d is the gap distance.)
 
So I made this question out to be harder it actually was. I was thinking about the changing electric field in the wrong way.

So here's my work:

Id = 0.80 x 10^-8 A
dE/dt = 1.5 x 10^6 V/m
ΦE = EA

Id = ε0(ΔΦE/Δt)
Id = ε0(A)(ΔE/Δt)
A = Id/[ε0 x (ΔE/Δt)]
A = 0.80 x 10^-8/(8.85 x 10^-12)(1.5 x 10^6)
A = πr2 = 6.03 x 10^-4 m2
r = 1.4 x 10^-2 m or 1.4 cm
 
Yes. You cannot actually determine the gap distance, because you're not told the voltage change rate.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Thread 'Egg Drop Challenge! Need ideas for winning designs'

I was thinking using 2 purple mattress samples, and taping them together, I do want other ideas though, the main guidelines are; Must have a volume LESS than 1600 cubic centimeters, and CAN'T exceed 25 cm in ANY direction. Must be LESS than 1 kg. NO parachutes. NO glue or Tape can touch the egg. MUST be able to take egg out in less than 1 minute. Grade A large eggs will be used.
View full post »

Similar threads

Finding Dimensions of plates in Electric Field
Replies
29
Views
2K
Find the dimension of capacitor given [phi]E and Id
Replies
5
Views
4K
Parallel-Plate Capacitor Separation
Replies
2
Views
1K
Max voltage of an air capacitor
Replies
4
Views
2K
Capacitance and Dielectrics in Parallel Plate Capacitors
Replies
2
Views
2K
Capacitors: find the dielectric constant
Replies
2
Views
1K
Determining speed of electron in a parallel plate capacitor
Replies
3
Views
9K
Parallel plate capacitor: Proton vs Electron
Replies
6
Views
14K
Total energy of charge in parallel plate capacitor
Replies
5
Views
2K
A dielectric-filled parallel-plate capacitor has plate area
Replies
1
Views
7K

Hot Threads

Recent Insights

Back
Top