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If the magnitude of the electric field in air exceeds roughly 3 脳 106 N/C, the air brake down and a spark form. For a two-disk capacitor of radius 47 cm with a gap of 1 mm, what is the maximum charge (plus and minus) that can be placed on the disks without a spark forming (which would permit charge to flow from one disk to the other)?

Short Answer

Expert verified

The maximum charge that can be placed on disk is 1.8410-5C.

Step by step solution

01

Identification of given data

The given data can be listed below,

  • The electric field of air is,E=3106N/C
  • The radius of capacitor is,R=47cm
  • The gap between two disk of capacitor is,d=1mm
02

Concept/Significance of capacitor.

When the voltage is supplied across the capacitor's metallic plates, a charge is stored electrostatically.

A capacitor is made up of two metallic plates separated by a dielectric substance. The charge is stored in the dielectric substance, which is non-conductive.

03

Determination of maximum charge be placed on disks

The electric field on the capacitor is given by,

E=qA0

Here, q is the charge on the disk, A is the area of disk and 0is the permittivity of free space.

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

q=EA0

role="math" localid="1656930383038" =3106N/C0.47m28.8510-12C2/N.m2=1.8410-5C

Thus, the maximum charge that can be placed on disk is role="math" localid="1656930441071" 1.8410-5C.

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A solid plastic sphere of radius R1has a charge -Q1on its surface (Figure 15.70). A concentric spherical metal shell of inner radius R2and outer radius R3carries a charge Q2on the inner surface and a charge Q3on the outer surface. Q1, Q2, and Q3are positive numbers, and the total charge Q2+Q3on the metal shell is greater than Q1.

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