A highly charged piece of metal (with uniform potential throughout) tends to spa

Question

A highly charged piece of metal (with uniform potential throughout) tends to spark at places where the radius of curvature is small, or at places where there are sharp points. The breakdown electric field strength for air is about 3*10^6 V/m.

(a) It is possible to calculate the maximum possible potential (relative to infinity) in air of a metal sphere of 4 cm radius. First, what is the maximum charge you can put on this sphere? (in columbs)

For that amount of charge, what is the potential of the sphere relative to infinity? (in volts)

Explanation / Answer

use the relation betweeen Elecric field and electric potnetial as

E = V/d

but here

we Can determine charge Q as Q =   E eo A

where E is electric field

eo is constant = 8.85 e-12

A is area =   pi r^2

here radius r = 4 cm   or 0.04 m

so

charge Max Qmax = 3e6 * 8.85 e-12 * 4*3.14 * 0.04*0.04

Qmax = 533.54 nC---------------------MAx charge

-----------------------------

now use the relation V = Ed

V = 3e6 * 0.04

V = 1.2 *10^5 Volts

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