Electrodynamics problem -- Calculating the resistance of ocean water

[LCSphysicist]

Homework Statement

The first telegraphic messages crossed the Atlantic in 1858, by a
cable 3000 km long laid between Newfoundland and Ireland. The
conductor in this cable consisted of seven copper wires, each of
diameter 0.73 mm, bundled together and surrounded by an insulating
sheath.

Relevant Equations

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A return path for the current was provided by the ocean itself.
Given that the resistivity of seawater is about 0.25 ohm-meter,
see if you can show that the resistance of the ocean return
would have been much smaller than that of the cable. (Assume
that the electrodes immersed in the water were spheres with
radius, say, 10 cm.)

I will not post my attempt to solve it because, actually, i have no idea what the question is talking about.
What i am suppose to do with this spheres in the water?

 

[Delta2]

I think the problem wants you to calculate the resistance of a cylindrical path of seawater that is 3000km long and has 10cm radius. But of course this is kind of absurd because when we immerse an electrode into sea , the signal path is not a narrow cylindrical path, instead the signal transmits spherically to all directions of the water.

EDIT: In view of the following posts i realized i was wrong, please ignore this post.

 

[hutchphd]

I think the 10 cm electrodes are included to imply they are not a high resistance chokepoint. So what is the resistance of the 3000 km wire?? How about a 2000km "slab" of ocean? Which is less?

 

[Delta2]

How about a 3000km "slab" of ocean?

What dimensions of width and depth are you going to take for this slab?

 

[hutchphd]

How about 1kmX10km and see where that puts you. So the area will be ##10^7m^2##. This is then ##10^{12}## the section area of the copper wire. I'll bet that wins by a lot.

 

[Delta2]

ok fine, but (here comes the question i was afraid to ask) why can't we achieve communication this way, say by putting one electrode (not just 10cm but i would say 10m long) at the harbor in New York and one at the harbor in ireland?

 

[Delta2]

I guess main reason is because anything can interfere along the ocean path from new york to ireland.

 

[Keith_McClary]

The resistance of the water between the 10 cm sphere and a larger sphere may be significant. You need to estimate that.

 

[haruspex]

ok fine, but (here comes the question i was afraid to ask) why can't we achieve communication this way, say by putting one electrode (not just 10cm but i would say 10m long) at the harbor in New York and one at the harbor in ireland?

Because you need a circuit.

 

[haruspex]

calculate the resistance of a cylindrical path of seawater that is 3000km long and has 10cm radius

No, that would probably be a significant resistance.
The path widens as an expanding sphere from each end, so the resistance along the path falls off quickly.
Consider a sphere of radius R held at voltage V and embedded in an infinite medium of given resistivity. The voltage at infinity is zero. What current flows?

 

[Delta2]

Consider a sphere of radius R held at voltage V and embedded in an infinite medium of given resistivity. The voltage at infinity is zero. What current flows?

That seems like an interesting problem i think we first need to calculate V(r) from r=0 to infinity.
But ,maybe the current is zero, unless we have some return path?

 

[haruspex]

But ,maybe the current is zero, unless we have some return path?

That the voltages at sphere and at infinity stay constant assumes a return path. You don't need to add one.