Max Charge Capacity on a Spherical Body: Calculating the Limit

[El Hombre Invisible]

Me again.

Is there a formula for the maximum amount of charge may be stored on a body (assume spherical) of radius r? I assume radius is the only factor, though mass is known also. I just don't remember seeing anything for this and can't find it in all my books for the life of me.

Thanks.

 

[himanshu121]

Lets try ::
Capacitance:: C=$$4 \pi \epsilon r$$
Q=CV
$$Q=4 \pi \epsilon r V$$
Now V should be less than E₀ Breakdown Voltage
so max can be
$$Q_{max} = 4 \pi \epsilon r E_0$$
Well I am not too sure abt above but its a try , if u can provide some other logic it will be welcomed

 

[El Hombre Invisible]

Lets try ::
Capacitance:: C=$$4 \pi \epsilon r$$
Q=CV
$$Q=4 \pi \epsilon r V$$
Now V should be less than E₀ Breakdown Voltage
so max can be
$$Q_{max} = 4 \pi \epsilon r E_0$$
Well I am not too sure abt above but its a try , if u can provide some other logic it will be welcomed

Dammit, sorry I was being dumb. I didn't notice we were given the electrical breakdown of air in the problem, so I know the maxmum electric field, I know the radius, and from this I can easily get the charge:

Q = $$4 \pi \epsilon r^2$$E(r)

Apologies for wasting thine time, and thanks for posting back. I was pretty tired. :zzz: Take care.