Question

Two identical closely spaced circular disks form a parallel-plate capacitor. Transferring 2.1×109 electrons from one disk to the other causes the electric field strength between them to be 1.5×105 N/C .
What are the diameters of the disks?

Answer 1

Answer:

$d = 0.018 m$

Explanation:

Charge on the plates of the capacitor due to transfer of electrons is given as

$Q = Ne$

here we know that

$N = 2.1 \times 10^9$

so we have

$Q = (2.1 \times 10^9)(1.6 \times 10^{-19})$

$Q = 3.36 \times 10^{-10} C$

now we have electric field between the plates is given as

$E = \frac{Q}{A\epsilon_0}$

here we have

$1.5 \times 10^5 = \frac{3.36 \times 10^{-10}}{A(8.85 \times 10^{-12})}$

$A = 2.53 \times 10^{-4} m^2$

now we have

$A = \frac{\pi d^2}{4}$

$2.53 \times 10^{-4} = \frac{\pi d^2}{4}$

$d = 0.018 m$