Help me calculate the charge of two circular plates

[jenko]

hi can anyone help me with this question?

the flux density between two circular places each of the radius 200mm is 10µCm. what is the charge of the plates?

this is what ive done:

Flux density D = Flux = coulombs/m²
Area

area of one plate = 125680 mm
two plates =251360 mm

flux
125680 = 10µCm INVERTED

0.000010x125680=1.2568 (FLUX)
Two plates =2.5136


what do i work out from here?

thank you!

 

[jenko]

Re: what do i do next?

anyone?

 

[mister_rf]

Re: what do i do next?

You need to consider only one plate for the area in use.

D = εE = ε * Q/π ε r²


D=Q/π r²
Q=D*π r²
r=200mm=0.2m
r²=0.04m²
Q=10µC/m² * π * 0.04m²=10*10exp-6*π* 0.04=1,256*10exp-6=1,256µC
Q=1.256µC

 

[subharpe]

Re: what do i do next?

You can proceed logically from Gauss's theorem. Consider a hypothetical closed surface which includes inside both the plates. Then because the flux lines start from one plate and terminate on the other and the lines go through the region in between the two plates the total flux going out of the hypothetical surface is zero. This means total charge contained insidde the surface is zero. Now because we are talking static charges (otherwise the flus lines would have varied with time) it is likely that one of the plates will contain as much positive charge as negative charge the other plate will contain. Assume that charge on each plate to be Q. Now to find the charge Q assume another cylindrical closed surface with the radius equal to the radius of the plates and the flat surface parallel to the plates with it's axix passing through the centre of the plates perpendicularly. Then the total flux entering the surface is given by the D in your problem. So what else is required? Simply apply Gauss's law and fing the charge.