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Anonymous119
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[Note from mentor -- this post was moved here from another forum]
Hi,
I ran to this problem today and i try to solve it but i can't complete it so if anyone can help me :)
Sphere has a charge Q0. Inside the sphere is vacuum and outside the air. Consume that air has small non zero conductivity s (the inverse of resistivity=1/ρ=s). Find how its charge
will evolve with time Q = Q(T).
Here is my work:
[itex]Q(T) = Q_0-dQ(T)[/itex]
[itex]dQ=\int_0^T I(t)\, dt[/itex]
where is I=U/R
R=1/s *l/S where l= dr(distance betwen our sphere(r) and sphere (r+dr)) where dr is very small and S=4pi*r^2
U=kQ(t)*(1/r-1/(r+dr))
When i arranged this i got:
I(t)=Q(t)*s/e0 so
[itex] dQ=\frac{s}{e_0} \cdot \int_0^TQ(t)dt [/itex]
[itex]Q(T)=Q_0-\frac{s}{e_0}\cdot\int_0^TQ(t)dt [/itex]
Where e0 is eletric constant.
And now i don't know how to solve this equation.
So please if anyone know how or see any mistake in my work post here.
Thanks !
Hi,
I ran to this problem today and i try to solve it but i can't complete it so if anyone can help me :)
Sphere has a charge Q0. Inside the sphere is vacuum and outside the air. Consume that air has small non zero conductivity s (the inverse of resistivity=1/ρ=s). Find how its charge
will evolve with time Q = Q(T).
Here is my work:
[itex]Q(T) = Q_0-dQ(T)[/itex]
[itex]dQ=\int_0^T I(t)\, dt[/itex]
where is I=U/R
R=1/s *l/S where l= dr(distance betwen our sphere(r) and sphere (r+dr)) where dr is very small and S=4pi*r^2
U=kQ(t)*(1/r-1/(r+dr))
When i arranged this i got:
I(t)=Q(t)*s/e0 so
[itex] dQ=\frac{s}{e_0} \cdot \int_0^TQ(t)dt [/itex]
[itex]Q(T)=Q_0-\frac{s}{e_0}\cdot\int_0^TQ(t)dt [/itex]
Where e0 is eletric constant.
And now i don't know how to solve this equation.
So please if anyone know how or see any mistake in my work post here.
Thanks !
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