What is the Significance of the Electric field in a closed circuit

[Muhammad Usman]

Hi,

I am confused about the electric field lines which are depicted mostly on the Internet as per conventional way.

What I understand that the conventional current was due to positive charges which was wrong. Actual flow of the current was due to the negative charges or electrons. When the conductor is connected with both terminal of the battery Positive ( Where the concentration of the positive charges are more) and negative (Excess of electrons or negative charge) charges the electric field is generated. Electric field itself is the influence of charge around it. Since there is net positive charge on one electrode of the battery and net negative charge on the another electrode, Electric field is generated around the electrodes. Now we have the property of the charges that similar charges repel and different charges (+ and -) attract each other. Since due to electric field influence and this property of the two different polarity charges attract the electrons started drifting from negative to the positive terminal of the battery due to force of attraction from the electric field. Correct me if I am wrong some where.

Now main problem is when I see the direction of electric field on the internet it is the convention from positive to the negative. this is really confusing me because as per force influence by electrons due to the polarity causing the electrons to flow from negative to positive terminal but the direction which is mentioned is from positive to negative. How is that possible that force direction is different and the particle which moved due to that force is in different direction ?

 

[tech99]

Hi,

I am confused about the electric field lines which are depicted mostly on the Internet as per conventional way.

What I understand that the conventional current was due to positive charges which was wrong. Actual flow of the current was due to the negative charges or electrons. When the conductor is connected with both terminal of the battery Positive ( Where the concentration of the positive charges are more) and negative (Excess of electrons or negative charge) charges the electric field is generated. Electric field itself is the influence of charge around it. Since there is net positive charge on one electrode of the battery and net negative charge on the another electrode, Electric field is generated around the electrodes. Now we have the property of the charges that similar charges repel and different charges (+ and -) attract each other. Since due to electric field influence and this property of the two different polarity charges attract the electrons started drifting from negative to the positive terminal of the battery due to force of attraction from the electric field. Correct me if I am wrong some where.

Now main problem is when I see the direction of electric field on the internet it is the convention from positive to the negative. this is really confusing me because as per force influence by electrons due to the polarity causing the electrons to flow from negative to positive terminal but the direction which is mentioned is from positive to negative. How is that possible that force direction is different and the particle which moved due to that force is in different direction ?

It is just a matter of definition. The electric field lines depict the path taken by a positive charge. So an electron, which is negative, will travel the opposite way.

 

[Dale]

Actual flow of the current was due to the negative charges or electrons.

I would stop you right there. The charge carriers in metals are negative but the charge carriers in batteries are often positive and charge carriers in biological tissues are also often positive. If the charge carriers are negative then the current flows in the opposite direction of the motion of the charge carriers, and if the charge carriers are positive then the current is in the same direction. But in the end it doesn’t matter for ordinary circuits, the fields produced by currents depend only on the current, not on the sign of the charge carrier.

Just think about conventional current and do not worry about electron motion. Current goes from the positive terminal to the negative terminal of an active battery, regardless of whether the conductive path is through a metal or through something else.

 

[ZapperZ]

I also want to add that redefining current to be the flow of negative charges does not solve anything. What about the times when there ARE positive charge flow? In a semiconductor, the majority charge carrier can be the positive holes. In particle accelerators, the moving charges can be positive particles such as protons and heavy ions. So one STILL has to point current in the opposite direction for these positive particles. In other words, same old issue.

So since we already have a well-established concept on how we define current, and since redefining it the other way doesn't solve anything or make anything simpler, I do not understand the brouhaha here.

Zz.

 

[Drakkith]

Now main problem is when I see the direction of electric field on the internet it is the convention from positive to the negative. this is really confusing me because as per force influence by electrons due to the polarity causing the electrons to flow from negative to positive terminal but the direction which is mentioned is from positive to negative. How is that possible that force direction is different and the particle which moved due to that force is in different direction ?

It's because field lines are NOT 'force lines'. They represent the electric field vector, and the electric field itself is a vector field. A vector field is just a way of labeling every point in space with a vector, which is a mathematical way of representing the direction and magnitude of something. For example, meteorologists use a vector field to represent the wind speed and direction at different locations. Each location would have a vector assigned to it where the magnitude of the vector represents the wind speed and the direction of the vector represents the direction the wind is blowing in. Since this vector field can be visualized as being arrows at every point, they can then draw lines to connects these arrows. These lines would then obviously represent the direction of the wind. We can do something similar with the electric field.

First we need to talk about Coulomb's law. In vector form, Coulomb's law is: $k_e\frac{q_1q_2}{|r_{12}|^2}r_{12}$ where $r_{12}$ is the unit vector pointing from charge 1 to charge 2, $q_1$ is the source charge, and $q_2$ is whatever charge you're interested in. To create the electric field, we divide out $q_2$ to make it so that the only charge in the general expression is the source charge, $q_1$ (which, when creating the electric field, is always positive by convention). This gives us the force per unit of charge at any location. In other words, to get the actual force on a charged particle you have to put the value for $q_2$ back into the expression, where $q_2$ is the charge of your charged particle.

Since $q_1$ and $q_2$ are multiplied by each other, if the two charges have like signs then the force is a positive quantity. However, if the two charges have opposite signs, then the result is negative and $r_{12}$ (remember, it's a vector) is multiplied by a negative number, turning the vector around so that it points in the opposite direction. The final result of the entire expression is a vector with its magnitude as the force on the charged particle and its direction as the direction of the force.

But! Remember that when we create the electric field we don't actually have $q_2$! We've divided it out! So our vector points away from our positive charge and it is this vector that the electric field lines represent, not the vector representing the force on an actual charged particle (since we don't even have a second charged particle yet!).

Once we have our electric field, we can then draw lines connecting the vectors. Using these lines we can easily visualize the reaction a test charge would have if placed anywhere in the field just by remembering that the line doesn't represent the electric force on our charged particle, it represents the electric field vector (basically Coulomb's law without the second charge, $q_2$).

To reiterate, the field lines do not represent a force. To get the actual force we need to put in our second charge, and that charge can be either positive or negative, with the negative charge feeling a force in the opposite direction of the field line.

 

[vanhees71]

There is a lot of confusion concerning the direction of currents. The cleanest way to define it is to use the current density
$$\vec{j}=\rho \vec{v},$$
where $\rho$ is the electric-charge sensity of the "charged fluid" and $\vec{v}$ its velocity field. If $\rho$ is negative as in usual metallic conductors, it's immediately clear that $\vec{j}$ points in the opposite direction than the fluid flow $\vec{v}$.

The sign of the current is then dependent on the arbitrary choice of the surface-normal vector of the surface (e.g., a cross section of a wire):
$$I=\int_A \mathrm{d}^2 \vec{f} \cdot \vec{j}.$$
The only thing which is important is that you keep the right-hand rule conventions concerning Stokes's theorem applied to Faraday's Law in order, as well as the sign in Ohm's law, which in its local version is also unambigous $\vec{j}=\sigma \vec{E}=-\sigma \vec{\nabla} \phi$, where $\phi$ is the static potential of the electric field.