Chapter 2: Q44 P (page 45)

If the magnitude of the electric field in air exceeds roughly $3 \times 10^{6} N 3$ , the air break down and a spark forms. For a two-disk capacitor of radius 51 cm with a gap of 2 mm, if the electric field inside is just high enough that a spark occurs, what is the strength of the fringe field just outside the center of the capacitor?

Short Answer

Expert verified

The electric field strength of fringe outside the centre of capacitor is $3 \times 10^{6} N / C$ .

Step by step solution

Identification of given data

The given data can be listed below,

The magnitude of electric field of air is, $E = \frac{q}{A ε_{0}} = 3 \times 10^{6} N / C$
The radius of disk is $R = 51 cm (\frac{1 m}{100 cm})$
The gap between two plates is, $r = 2 mm (\frac{1 m}{1000 mm})$

Concept/Significance of capacitor

the capacitor has an insulator (dielectric) inside it that prevents any charge flow through itself, so the two faces of the dielectric get charged when you charge the capacitor.

Determination of the electric field strength of fringe outside the center of capacitor

The electric field of fringe is given by.

The electric field on the capacitor is given by,

$E = \frac{q}{2 A ε_{0}} \frac{r}{R}$

Here, $q$ is the charge on the disk, A is the area of disk, r is the distance between two disks and $ε_{0}$ is the permittivity of free space.

Substitute all the values in the above equation,

$E_{f r i n g e} = \frac{1}{2} (3 \times 10^{6} N / C) \frac{2 \times 10^{- 3} m}{0.51 m} = 5.88 \times 10^{3} C$

Thus, the electric field strength of fringe outside the centre of capacitor is $3 \times 10^{6} N / C$ .

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Short Answer

Step by step solution

Identification of given data

Concept/Significance of capacitor

Determination of the electric field strength of fringe outside the center of capacitor

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