- #1
tronter
- 183
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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?
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?
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