Question

A circular parallel-plate capacitor with a spacing of 1.6 mm is charged to produce a uniform electric field with a strength of 2.7 × 106 N/C. What plate radius is required if the stored charge is −1.07 µC? The permittivity of a vacuum is 8.8542 × 10−12 C2/N · m2. Answer in units of m.

Answer 1

r = 0.119 m

Step-by-step explanation:

distance (d) = 1.6 mm = 0.0016 m

electric field strength (E) = 2.7 x 10^{6} N/C

charge (Q) = -1.07 μC = -1.07 x 10^{-6} C

permitivity of vacuum = 8.8542 x 10^{-12} C^{2}/N

find the radius of the plate required

• lets first find the voltage

voltage (V) = E x d

voltage (V) = 2.7 x 10^{6} x 0.0016 = 4320 V

• lets also find capacitance (C) = Q/V

C = -1.07 x 10^{-6} / 4320 = 2.47 x 10^{-10} F

• the value of capacitance (C) is also = E₀A / d

we can rearrange the equation above to have our area (A) = Cd/ E₀

A =
`(2.47 x 10^(-10) x 0.0016)/(8.8542 x 10^(-12))`

A = 0.0446 m^{2}

• Area (A) = π x
  `r^(2)`

r =
`\sqrt{(a)/(π) }`

r =
`\sqrt{(0.0446)/(π) }`

r = 0.119 m