Salty water resistance! slaughter the Fishes!

Electricity and Magnetism Level 5

Two identical metal balls of spherical shape in the sea water, and radius have been put in an infinite medium of conductivity σ \sigma .They are placed on a distance much bigger than their radius are. we want to know the resistance so we may know how much voltage we need to put so we can kill the fish,Show that Resistance can be expressed as R = γ ( σ k r δ ) R=\gamma (\sigma^k r^\delta) where γ , k , δ \gamma ,k,\delta is non dimensional constants that you should calculate.

What is ⌊ 100 γ + δ + k ⌋ ⌊100γ+δ+k⌋ ?

Hint: Ohm's law is J = σ E J=\sigma E .


The answer is 13.

Jafar Badour by jafar badour , 23, Russia

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1 solution

Jafar Badour
Oct 9, 2015

Δ U = q 2 π ϵ 0 r \Delta U= \frac{q}{2\pi\epsilon_0 r}

E = q 4 π ϵ 0 r 2 E= \frac{q}{4\pi\epsilon_0 r^2}

J = σ E → J = σ q 4 π ϵ 0 r 2 J=\sigma E\rightarrow J= \frac{\sigma q}{4\pi\epsilon_0 r^2}

the current equals i = J A i=JA while A = 4 π r 2 A=4\pi r^2 so

i = σ q ϵ 0 i= \frac{\sigma q}{\epsilon_0}

and we know that Δ U = R i \Delta U= Ri

so R = Δ U ϵ 0 σ q R=\frac{\Delta U\epsilon_0}{\sigma q}

R = 1 2 π σ r R=\frac{1}{2\pi\sigma r}

R = 0.159 σ − 1 r − 1 R=0.159\sigma^{-1} r^{-1}

so ⌊ 100 ∗ 0.159 − 1 − 1 ⌋ = 13 ⌊100*0.159-1-1⌋=13

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Could you please explain the solution? I didn't understand it how you got the expression for ∆U and E. Thanks.

Pranav Rao - 5 years, 5 months ago

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they are basics in electricity I recommend ("introduction to electrodynamics for david griffith ") study this book it contains all you need

jafar badour - 5 years, 4 months ago

Could you please explain how you got ∆U and ∆E.

Chirag Singapore - 5 years, 4 months ago

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