- #1
Titan97
Gold Member
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Homework Statement
If ##\vec{E}=k\frac{x\hat i +y\hat j}{x^2+y^2}##, find flux through a sphere of radius R centered at origin.
Homework Equations
##\int E.da=\int(\nabla\cdot E)\cdot da##
The Attempt at a Solution
I was able to solve this problem without finding divergence of electric field.
If ##\vec{r}= {x\hat i +y\hat j}##.
Then, $$E=k\frac{\vec{r}}{r^2}=k\frac{\hat r}{r}$$
This is like the electric field due to an infinite line charge which is given by $$E=\frac{\lambda}{2\pi\epsilon_0 r}$$
So the field specified in question can be assumed to be from an infinitely long charged wire.
I can easily find the flux using Gauss' law by finding the charged enclosed by the spherical surface.
But when I tried finding the divergence of E, it came out to be zero.
I used the formula $$E=\frac{\partial E}{\partial x}+\frac{\partial E}{\partial y}$$