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Two closely spaced circular disks form a parallel-plate capacitor. Transferring 1,675,802,144.45 electrons from one disk to the other causes the electric field strength to be 926,331.13 N/C. What are the diameters, in mm, of the disks?

Sagot :

The electric field between the plates of a capacitor (assuming it is closely spaced) is given by:

[tex]\vec{E}=\frac{Q}{\epsilon_0A}[/tex]

We can replace our values, and we'll get the following:

[tex]926331.13=\frac{1675802144.45*1.6*10^{-19}}{8.8541878*10^{-12}A}[/tex]

By isolating the are, we get:

[tex]A=\frac{1675802144.45*1.6*10^{-19}}{8.8541878*10^{-12}*926331.13}=3.269*10^{-5}m^2[/tex]

Now, if we replace it on the area of a circle:

[tex]3.269*10^{-5}=\pi r^2[/tex]

Our value of r is:

[tex]r=\sqrt[\placeholder{⬚}]{\frac{3.269*10^{-5}}{\pi}}=3.2258mm[/tex]

Then, our final answer is d=6.4515mm

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