Work done by moving unit charge along straight line segment

[tronter]

If $$\bold{F}(x,y) = \frac{k(x \bold{i} + y \bold{j})}{x^{2}+y^{2}}$$ find the work done by $$\bold{F}$$ in moving a unit charge along a straight line segment from $$(1,0)$$ to $$(1,1)$$.

So $$\bold{F}(1,y) = \frac{k(\bold{i} + y \bold{j})}{1 + y^{2}}$$. Then $$x = 1, \ y = y$$.

$$k \int_{0}^{1} \frac{y}{1+y^{2}} \ dy$$

$$u = 1+y^{2}$$

$$du = 2y \ dy$$

$$\frac{k}{2} \int \frac{du}{u}$$

$$= \frac{k}{2} \int_{0}^{1} \ln|1+y^{2}|$$

$$= \frac{k\ln 2}{2}$$.

Is this correct?

 

[HallsofIvy]

Looks perfectly good to me.