Why Does a Charged Disk Generate a Non-Zero Electric Field at Its Center?

[hell-hawk]

I have two questions.
The first concerns a charged disk. Consider the center of the surface of the charged disk, O. Mathematically, the value of E at O comes out to be a non-zero finite value. However i am having difficulty linking this with the physical sense. The disk can be thought to be composed of an infinite number of rings; i think that each ring will set up zero electric field at O since for each charge element on the ring, the diametrically opposite charge element of the charge element cancels its effect. So how come does E come out to be non-zero at O? Please explain the flaw in my reasoning in physical terms, not mathematical.
The second question involves two charges. Consider one charge to be fixed, while the other moves past it in a straight line. What fields will be set up?
What force, if any, will act on each of the charges?
Please help. I'll be highly grateful.

 

[ZapperZ]

I have two questions.
The first concerns a charged disk. Consider the center of the surface of the charged disk, O. Mathematically, the value of E at O comes out to be a non-zero finite value. However i am having difficulty linking this with the physical sense. The disk can be thought to be composed of an infinite number of rings; i think that each ring will set up zero electric field at O since for each charge element on the ring, the diametrically opposite charge element of the charge element cancels its effect. So how come does E come out to be non-zero at O? Please explain the flaw in my reasoning in physical terms, not mathematical.

What if I put a point charge at O? Do you still expect to measure a non-zero E-field there? If you do, then no matter how many of these rings you add, even if the fields for these rings cancel, you will have a net field from this point charge at O. So you should think of a disk as being assembled by all of these rings, except that the ring of infinitesimal diameter at the origin approaches that of a point charge.

Zz.

 

[Graeme Robinson]

Firstly, it is important to understand that the mathematical equation for electric field (E) at a point is a vector sum of all the electric fields produced by individual charge elements. This means that even though each individual charge element may produce a zero electric field at point O, the sum of all these individual fields may result in a non-zero value at point O. This is due to the fact that the electric field is a vector quantity and its direction and magnitude can change based on the position and orientation of the charged disk.

To explain this in physical terms, imagine a disk with a positive charge distributed on its surface. As you correctly stated, each individual charge element on the disk will produce an electric field that is canceled out by the diametrically opposite charge element. However, as you move closer to the center of the disk, the electric field produced by the charge elements on the outer edge of the disk will have a greater effect on the overall electric field at point O than the charge elements closer to the center. This is because the electric field decreases with distance, and the closer you get to the charge elements, the smaller the contribution they make to the overall electric field. Therefore, the sum of all these individual fields, taking into account their direction and magnitude, will result in a non-zero value at point O.

Moving on to your second question, when two charges are present, they will interact with each other through their electric fields. The fixed charge will produce an electric field that will exert a force on the moving charge, causing it to accelerate towards or away from the fixed charge depending on their respective charges. At the same time, the moving charge will also produce its own electric field, which will exert a force on the fixed charge. This force will be equal in magnitude but opposite in direction to the force acting on the moving charge, as per Newton's third law of motion.

In summary, the electric field at a point is the vector sum of all the individual electric fields produced by the charges in the vicinity, and when two charges are present, they will interact with each other through their electric fields, resulting in a force acting on each of the charges. I hope this helps to clarify your understanding of electromagnetism.