Match the vector field with its plot.
$$\mathbf { F } ( x , y ) = \frac { x } { x ^ { 2 } + y ^ { 2 } } \mathbf { i } - \frac { y } { x ^ { 2 } + y ^ { 2 } } \mathbf { j }$$

Question

Quizplus · Accepted Answer

The given vector field is equivalent to $\mathbf {F}(r,	heta) = \frac{1}{r}\mathbf{i}-\frac{1}{r}\mathbf{j}$ in polar coordinates. This vector field has a constant magnitude of $\frac{1}{r}$ and points radially inward towards the origin at every point except for the origin itself where the vector field does not exist. Therefore, the plot should show equally spaced vector lines pointing inward towards the origin, and the vectors should get longer as the distance from the origin decreases. Option D is the only plot that fits this description.

Match the Vector Field with Its Plot F(x,y)=xx2+y2i−yx2+y2j\mathbf { F } ( x , y ) = \frac { x } { x ^ { 2 } + y ^ { 2 } } \mathbf { i } - \frac { y } { x ^ { 2 } + y ^ { 2 } } \mathbf { j }F(x,y)=x2+y2x​i−x2+y2y​j

Match the Vector Field with Its Plot $\mathbf { F } ( x , y ) = \frac { x } { x ^ { 2 } + y ^ { 2 } } \mathbf { i } - \frac { y } { x ^ { 2 } + y ^ { 2 } } \mathbf { j }$