Electric field of line of charge

[chessmath]

Hi
Is electric field zero or undefined?

 

[Doc Al]

Hi
Is electric field zero or undefined?

At what point? Where along the line of charge is point B?

 

[chessmath]

You can clearly see point B is the middle of line of charge with length L. so now question is what is field at this point?

 

[Doc Al]

You can clearly see point B is the middle of line of charge with length L.

Too bad you didn't clearly label that point as being exactly in the middle.

so now question is what is field at this point?

What do you think? (Why would you think it would be undefined?)

 

[chessmath]

Because electric field is defined in the area around line of charge not on the line of charge.2- when you take integral you get infinity meaning that it is not defined.

 

[Doc Al]

when you take integral you get infinity meaning that it is not defined.

Show the integral you are taking.

 

[chessmath]

it is the integral of 1/x^2 from 0 to L/2. meaning that putting value of 0 make the integral infinity.

 

[Doc Al]

it is the integral of 1/x^2 from 0 to L/2. meaning that putting value of 0 make the integral infinity.

Ah yes, you're right. But by symmetry we know that the field in the middle must be zero--the two halves will cancel out.

 

[chessmath]

You are right. But there is second argument that says electrif field is defined in the surronding of line of charge or point charge and not on itself. that's why it is undefined.