Question

What is amount of charge flown due to connection of two parallel charged plates?

Answer 1

Answer:

❤️❤️You start with a total of 3Q on the outer plates - and that charge has nowhere to go. So when you connect the two plates together, they will share the charge equally, and have a net charge of 1.5Q on each. Grounding the center plate means that charge can flow freely. So what will happen?

First - charge will flow between plate B and ground. The boundary conditions are:

Potential of A and C will end up being the same (they are connected)

Potential of B will be zero (it is grounded)

Charge will distribute according to the capacitance. Since

Q=C.V

and

C=kϵ0Ad

We find

Q1C1=Q2C2

or

Q1d1=Q2d2

We also have

Q1+Q2=3Q

So given that

d2=2d1

it follows that the charge on the inside of the plates is

q1=2Qq2=Q

The plate B will accumulate a charge of −3Q in order to exactly cancel the 3Q charge on the outer plates. Why? Well - if there is a residual charge, there will be an electric field. Electrons "in the ground" will either be pulled towards the plates (if net charge is positive) or repelled (if it is negative). Their movement will adjust the charge on plate B until there is no field - at that point, there is no energy to be gained by charges moving. You have reached equilibrium.

When all is done, the charge distribution will be:

0 on the outside of A and C

2Q on the inside of A

Q on the inside of C

−2Q on the left side of B

−Q on the right side of B

The net charge on the system is zero. Thus

∇E=0

which implies that the surface charge on the outside of the plates must also be zero.❤️❤️

Step-by-step explanation:

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