Two circular disks spaced 0.50 mm apart form a parallel-plate capacitor. transferring 1.70 x 10^9 electrons from one disk to the other causes the electric field strength to be 2.60 x 10^5 n/c. what are the daimeters of the disk?

The diameters of the disk is 1.23 cm

Explanation:

Given information:

the space of two disks, d =0.5 mm = 0.0005 m =  5 x m

the transferred electron, n = 1.70 x

electric field strength, E = 2.6 x N/C

to find the diameter of the disk we can use the following equation

A = πD²/4 ...........................................(1)

where

D = the distance of the disk

A = the area of the disk

first, we have to find the are of the disk using the capacitance equation

C = ε₀A/d...........................................(2)

A = Cd/ε₀ where C = Q/V (Q is total charge and V is potential difference)

thus

A = Qd/Vε₀.........................................(3)

now substitute V = Ed and Q = ne, so

A = (ned)/(Edε₀)

   = ne/Eε₀..........................................(4)

e = 1.6 x C

now can substitute equation (4) to the first equation

A = πD²/4

D² = 4A/π

D  = √4A/π

    = √(4ne)/(πEε₀) , ε₀ = 9.85 x C²/Nm²

    = √4(1.70 x )(1.6 x )/π(2.6 x )(8.85 x )

    = 0.0123 m

    = 1.23 cm

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explanation:

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