All Problems

Constant Electric Field in a Vacuum

Problem 3.36

Determine the electric field strength vector if the potential of this field depends on x,yx, y coordinates as a) φ=a(x2−y2)\varphi=a\left(x^{2}-y^{2}\right) (b) φ=axy\varphi=a x y where aa is a constant. Draw the approximate shape of these fields using lines of force (in the x,yx, y plane).

Reveal Answer
3.36. (a) E=−2a(xi−yj)\mathbf{E}=-2 a(x \mathbf{i}-y \mathbf{j}) (b) E=−a(yi−xj)\mathbf{E}=-a(y \mathbf{i}-x \mathbf{j}). Here i\mathbf{i} are the unit vectors of the xx and yy axes. See Fig. 16 illustrating the case a>0a>0
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