Question

The elctric potential in two dimensional near an object , located at the origin carrying charge Q is given by V= KQ/(x^2+y^2)^1/2 where K is constatnt . find the component of the electric field Ex and Ey at some general set of coordinates (x,y). what can you say about the magnitude and direction of the field?...i have a grap for coordinates

Answer 1

Question #15043

Given $V = kQ\sqrt{x^2 + y^2}$ , we obtain: $\vec{E} = -\nabla V = -kQ\left(\frac{x}{\sqrt{x^2 + y^2}}, \frac{y}{\sqrt{x^2 + y^2}}\right)$ . The magnitude is $|\vec{E}| = kQ\sqrt{\frac{x^2}{x^2 + y^2} + \frac{y^2}{x^2 + y^2}} = kQ$ . We can see, the potential is spherically-symmetric, so the field goes into the center of the xy plane. Here is the sketch of a vector field: