Understanding the Radial Field Generated by an Infinite Line of Charge

[Seraph404]

"Stopping the Proton"

Homework Statement

An infinitely long line of charge has a linear charge density of 8.00×10−12 C/m. A proton is at distance 14.0 cm from the line and is moving directly toward the line with speed 1500 m/s.

I just want a better understanding of this statement:

"An infinite line of charge will generate a field with only a radial component."

Why, again? I can post more parts of the problem if that's too confusing.

 

[LowlyPion]

Because the line charge is infinite, the field lines will all be perpendicular to the wire - radially outward for plus charge - if for no other reason than that any calculation of the field will find as much charge to one side as to the other and any component of the field that might be calculated for charge on one side is canceled out by the field component from an equal charge an equal distance to the other. The equipotential surfaces will then be concentric cylinders.

 

[nlightner]

I can explain the concept of a radial field generated by an infinite line of charge.

Firstly, let us understand what an electric field is. An electric field is a region in space where a charged particle experiences a force due to the presence of other charged particles. The direction of the force experienced by the particle is determined by the direction of the electric field.

Now, coming to an infinite line of charge. An infinite line of charge has an infinite length, which means that it has an infinite number of charges distributed along its length. In this case, the line of charge has a linear charge density of 8.00×10−12 C/m, which means that for every meter of the line, there is a charge of 8.00×10−12 C.

When a charged particle, in this case a proton, is placed near the infinite line of charge, it will experience a force due to the presence of the charges on the line. This force is known as the electric force.

Now, the statement "an infinite line of charge will generate a field with only a radial component" means that the electric field generated by the infinite line of charge will only have a component in the direction of the line. This is because the charges on the line are uniformly distributed along its length, and their contribution to the electric field at any point will only be in the direction of the line.

To understand this further, imagine a point on the line of charge and a point directly above it. At both these points, the electric field generated by the charges on the line will be directed radially outward, perpendicular to the line. This is true for all points on the line and above it, hence the statement that the field has only a radial component.

In the context of the problem, the proton is moving directly towards the line of charge, which means that it will experience a force only in the radial direction. This force will cause the proton to decelerate or "stop" as it approaches the line of charge.

I hope this explanation helps you understand the concept of a radial field generated by an infinite line of charge. Please let me know if you have any further questions.