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Consider the following conclusiond regarding the components of an electric field at a certain point in space given by E_x = -Ky, E_y = Kx, E_z = 0 . |
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Answer» The field is conservative. Let us find potential difference between any two points: `V_(2)-V_(1)=-underset(x_(1))overset(x_(2))intE_(x)DX-underset(y_(1))overset(y_(2))intE_(y)dy` `RARR V_(1)-V_(1)=+underset(x_(1))overset(x_(2))intK_(y)dx-underset(y_(1))overset(y_(2))intK_(x)dy` This can further be evaluated only if we know the dependance of `x` and `y` on each other or the PATH of intergration. Hence field is nonconservative. To find the shape of lines of force: `tantheta=(E_(y))/(E_(x))` or `(dy)/(dx)=(E_(y))/(E_(x))` or `(dy)/(dx)=(K_(x))/(-K_(y))` or `xds+ydy=0` or `(x^(2))/(2)+(Y^(2))/(2)=C` or `x^(2)+y^(2)=2C` This is the equation of circle. 
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