Question

A capacitor consists of two large metal disks of radius 1.1 m placed parallel to each other, a distance of 1.2 mm apart. The capacitor is charged up to have an increasing amount of charge +Q on one disk and −Q on the other. At about what value of Q does a spark appear between the disks?

Short answer

The value of Q at which spark appear between disks is$1.009\times {10}^{-4}\mathrm{C}$ .

Step-by-step solution

Identification of given data

The given data can be listed below,

• The radius of metal disk is,R=1.1 m
• The distance between two disk is,d=1.2mm
• The maximum electric field of air is, $E=3\times {10}^8\mathrm{N}/\mathrm{C}$

Concept/Significance of charging of capacitors

A parallel plate capacitor is made up of two big planar parallel conducting plates separated by a tiny distance, each of which is linked to wires that are separated from one another by a thin area that can be a vacuum or a dielectric substance but not a conductor.

Determination of value of Q does a spark appear between the disks

The electric field of capacitor is given by,

$E=\frac{Q}{2{\epsilon }_0}$

Here, q is the charge on the disk, A is the area of disk and${\epsilon }_0$ is the permittivity of free space.

Substitute all the values in the above equation, the charge on the disk is given by,

$$\begin{gathered} Q=EA{\epsilon }_0 \\ =\left(3\times {10}^6\mathrm{N}/\mathrm{C}\right)\pi {\left(1.1\mathrm{m}\right)}^2\left(8.85\times {10}^{-12}{C}^2/N.{\mathrm{m}}^2\right) \\ =1.009\times {10}^{-4}\mathrm{C} \end{gathered}$$

Thus, the value of Q at which spark appear between disks is $1.009\times {10}^{-4}\mathrm{C}$.