- #1

- 1,169

- 132

- Homework Statement
- Please see below

- Relevant Equations
- Please see below

For this problem,

However, I am trying to solve this problem using an alternative method compared with the solutions. My method is:

##\vec E = k_e \int \frac {dq} {r^2} \, dx ## ##\hat r##

##\vec E = k_e \int \frac {\lambda} {x^2 + d^2} \, dx## ## \hat r##

If I let ## \hat r = \frac {-x\hat i + d\hat j} {\sqrt {x^2 + d^2}}## then I get the same answer as the solutions.

However, how dose ## \hat r = \frac {-x\hat i + d\hat j} {\sqrt {x^2 + d^2}}##?

I see intuitively that the ##\hat r## dose point in the same direction as the ##d\vec E## for each charge segment ##dq##.

Many thanks!

However, I am trying to solve this problem using an alternative method compared with the solutions. My method is:

##\vec E = k_e \int \frac {dq} {r^2} \, dx ## ##\hat r##

##\vec E = k_e \int \frac {\lambda} {x^2 + d^2} \, dx## ## \hat r##

If I let ## \hat r = \frac {-x\hat i + d\hat j} {\sqrt {x^2 + d^2}}## then I get the same answer as the solutions.

However, how dose ## \hat r = \frac {-x\hat i + d\hat j} {\sqrt {x^2 + d^2}}##?

I see intuitively that the ##\hat r## dose point in the same direction as the ##d\vec E## for each charge segment ##dq##.

Many thanks!

Last edited: