Question

a)

The following vector field $\overrightarrow{F}(x, y)$

State whether the divergence of $\overrightarrow{F}(x, y)$ at point A is positive, negative or zero.

b) Say if the rotational of $\overrightarrow{F}(x, y)$ at point B is a null vector, which points in the direction of the z-axis or points in the negative direction of z.

履 2 0 2 4

Answer 1

1.In Case of Point A , Strength of Field Going out from A is higher compared to the ones coming in.Net Influx<Net

Outflux.So , Net Flow=Net Outflux-Net Influx >0.So , resultant is outflux.So Divergence is positive.

2.So at point B, Vectors are pointing along a particular direction(fixed direction).There is no sense of rotation at the point.The Vectors are not curling or turningSo ,the rotational or curl must be zero vector or null vector.