# Electric field of line of charge

1. Oct 27, 2012

### chessmath

Hi
Is electric field zero or undefined?

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2. Oct 27, 2012

### Staff: Mentor

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

3. Oct 27, 2012

### 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?

4. Oct 27, 2012

### Staff: Mentor

Too bad you didn't clearly label that point as being exactly in the middle.
What do you think? (Why would you think it would be undefined?)

5. Oct 27, 2012

### 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.

6. Oct 27, 2012

### Staff: Mentor

Show the integral you are taking.

7. Oct 27, 2012

### chessmath

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

8. Oct 27, 2012

### Staff: Mentor

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.

9. Oct 27, 2012

### 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.