Confused about direction of electric field

[Muhammad Usman]

TL;DR Summary: I am studying a book and at some point i couldn't able to understand a topic about Electric field

hi All,

Currently I am reading a book "Matters and interactions". In chapter 18 - Page 724 author asked reader to do the exercise about the electric field in the wire. here are the exact words below:-

"At the locations marked X on a copy of Figure 18.16 (locations 1 through 5), draw arrows representing the approximate electric field due solely to the charges on the metal plates of the mechanical battery. (The amount of charge on the belt is completely negligible compared to the charge on the plates.) Forget the presence of the wire for the moment."

Next he asked for another exercise which is " Next, in a different color or with a different-looking arrow, indicate the drift velocity of the mobile-electron sea at those locations, assuming that the drift velocity is due solely to the electric field made by the charges on the plates of the mechanical battery"

and then in very next paragraph he mentioned about the electric field at point # 4 which doesnt make sense how did he calculate

"Good grief! Figure 18.17 shows that we’ve got the electron current running upstream at location 4 in the wire! That can’t be right in the steady state (the situation in which charge distributions and currents are not changing). We are forced to conclude that in the steady state there must be some other charges somewhere that contribute to the net electric field in such a way that the electric field points upstream everywhere (giving an electron drift velocity downstream everywhere)."

If we check the electric field it is from positive to negative plate and here if we see the location of electric field at point 4, it is towards the negative terminal of the battery, but in the very next figure in 18.17 (mentioned above) author takes the electric field in opposite direction (from negative to positive), technically he should not have done that and I dont understand his logic at point 4 that why he takes the direction of electric field in opposite direction, technically at point 4 it should not be towards the positive plate of the battery. Can any one understand this ?? please help

 

[Drakkith]

but in the very next figure in 18.17 (mentioned above) author takes the electric field in opposite direction (from negative to positive), technically he should not have done that and I dont understand his logic at point 4 that why he takes the direction of electric field in opposite direction, technically at point 4 it should not be towards the positive plate of the battery.

Sorry, I don't see where the author has done this. The figure clearly shows the electric field pointing to the right, just as it should be if we only consider the electric field of the 'battery'.

This, of course, can't be true if we are in a steady state situation, as that would cause electrons to move the wrong way in the wire. So the author concludes that there must be other charges that cause the electric field to point in the opposite direction (from right to left) that cause the electrons to move from left to right.

 

[Muhammad Usman]

Got it mate

 

[vanhees71]

I find the picture utmost confusing. I've no clue what the author wants to say and particularly I don't see, how the author comes to the directions of his vectors (drift velocities and electric fields). Wikipedia gets it much better:

https://en.wikipedia.org/wiki/Galvanic_cell

 

[Muhammad Usman]

Author has given lecture on this subject and i found these lectures online, here is the notes which I prepared after understanding what is happening

"A dipole is a separation of opposite electrical charges and it is quantified by an electric dipole moment. The electric dipole moment associated with two equal charges of opposite polarity separated by a distance 'd' is defined as the vector quantity having a magnitude equal to the product of the charge and the distance between the charges and having a direction from the negative to the positive charge along the line between the charges. This means that the electric field convention is taken right from negative to positive terminal of the battery because battery is being treated as the dipole. And the electric field at any location will be calculated by super-position principle and the direction of the electric field will be taken from positive to negative. Now lets think that each of the plate is a charge and if we calculate the net electric field at each point in the wire, it will be calculated by using the magnitude and the direction will be taken according to the vector addition, if we take this principle then we can find out that at location 4 the electric field is in the direction towards the positive terminal of the battery and then we calculate the drift speed then we can see it is always opposite of the E direction and there we can see the electrons will going into the left bend not going out"

 

[vanhees71]

The electric field is always pointing away from positive charges and towards negative charges by convention: $\vec{\nabla} \cdot \vec{E}=+\rho$.

 

[Drakkith]

I find the picture utmost confusing. I've no clue what the author wants to say and particularly I don't see, how the author comes to the directions of his vectors (drift velocities and electric fields).

The diagram doesn't include the field lines, which would make things MUCH clearer. I expect this is because they are supposed to be drawn by the student. If drawn, the field lines make the usual 'figure eight' and match with the vectors shown on the diagram as far as I can tell.

 

[kuruman]

I think that the "battery" in the figure that is made to resemble a parallel plate capacitor is a red herring. Current will flow in the serpentine wire just the same if the wires from a battery were soldered to its ends establishing a potential difference across. The picture of why current flows is not hard to understand. Assuming that the wire is electrically neutral, an electron in the wire moves towards the positive end of the battery leaving a positive "hole" which is filled by the negative electron behind it, which leaves another positive hole for a third negative electron behind the second $\dots$ and so on. It's a bit like squeezing a tube of toothpaste at its end. The paste that you squeeze at one end is not the paste that comes out the other end.

Imagine placing the entire nichrome wire between the plates of a charged capacitor with the switch connecting to the battery in the OPEN position. Some of the electrons in the wire will redistribute themselves until equilibrium is reached and the wire is an equipotential. There will be an induced surface charge density $\sigma(x,y)$ on the wire. Now flip the switch to the CLOSED position. What will happen? The surface charge distribution will be the same as before. Current will flow in the wire as if the external field were not there in a manner described in the previous paragraph. If you squeeze a toothpaste tube, toothpaste will come out whether you are in a gravitational field or not.

The use of the uniform electric field in the explanation is superfluous and confusing.