Question

Write a formula for a two-dimensional vector field which has all vectors parallel to the xx-axis and all vectors on a horizontal line having the same magnitude

Answer 1

`f(x,y)=u(y)\hat{i}`

Explanation:

Let two- dimensional vector field

`f(x,y)=u(x,y)\hat{i}+v(x,y)\hat{j}`

We have to find the formula for a two-dimensional vector field which has all vectors parallel to the x-axis and all vectors on a horizontal line having the same magnitude.

When all vector parallel to x- axis then

v(x,y)=0

Then, the vector field can be written as

`f(x,y)=u(x,y)\hat{i}`

When all vectors on a horizontal line having the same magnitude then

u(x,y)=u(y)

Substitute the values

Then, we get

`f(x,y)=u(y)\hat{i}`