- #1
tronter
- 183
- 1
If [tex]\bold{F}(x,y) = \frac{k(x \bold{i} + y \bold{j})}{x^{2}+y^{2}}[/tex] find the work done by [tex]\bold{F}[/tex] in moving a unit charge along a straight line segment from [tex](1,0)[/tex] to [tex](1,1)[/tex].
So [tex]\bold{F}(1,y) = \frac{k(\bold{i} + y \bold{j})}{1 + y^{2}}[/tex]. Then [tex]x = 1, \ y = y[/tex].
[tex]k \int_{0}^{1} \frac{y}{1+y^{2}} \ dy[/tex]
[tex]u = 1+y^{2}[/tex]
[tex]du = 2y \ dy[/tex]
[tex]\frac{k}{2} \int \frac{du}{u}[/tex]
[tex]= \frac{k}{2} \int_{0}^{1} \ln|1+y^{2}|[/tex]
[tex]= \frac{k\ln 2}{2}[/tex].
Is this correct?
So [tex]\bold{F}(1,y) = \frac{k(\bold{i} + y \bold{j})}{1 + y^{2}}[/tex]. Then [tex]x = 1, \ y = y[/tex].
[tex]k \int_{0}^{1} \frac{y}{1+y^{2}} \ dy[/tex]
[tex]u = 1+y^{2}[/tex]
[tex]du = 2y \ dy[/tex]
[tex]\frac{k}{2} \int \frac{du}{u}[/tex]
[tex]= \frac{k}{2} \int_{0}^{1} \ln|1+y^{2}|[/tex]
[tex]= \frac{k\ln 2}{2}[/tex].
Is this correct?
Last edited: