Electric field?
please solve the question and explain?
please solve the question and explain?
1 Answer
I get
(A) and (C)
Explanation:
Given electric field intensity at a point
Let's examine the case of a two-dimensional vector field whose
For the given field we have
As scalar curl
We know that potential in an two dimensional electric field is expressed as
vecE=-[hatidel/(delx)+hatjdel/(dely)]V(x,y)
For the given electric field above
-(delf)/(delx)=(12xy^3-4x) ....(1) and-(delf)/(dely)=18x^2y^2 .....(2)
From equation (1) using partial integration
-f(x,y)=int(12xy^3-4x)dx
=>-f(x,y)=(12xxx^2/2y^3-4xxx^2/2+C(y))
whereC(y) is a constant of integration dependent ony .
=>-f(x,y)=(6x^2y^3-2x^2+C(y))
Differentiating this with respect to
-(delf(x,y))/(dely)=-del/(dely)(6x^2y^3+2x^2+C(y))=-18x^2y^2
=>(6x^2 (3y^2)+d/dyC(y))=18x^2y^2
=>d/dyC(y)=0
=>C(y) is actually a constant independent of bothx and y .
The potential function becomes
f(x,y)=(6x^2y^3-2x^2+c)
Given that at origin electric potential is zero. Therefore
f(x,y)=6x^2y^3-2x^2 ......(3)
Therefore, electric potential at point
-f(1,1)=-4V
.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
A two dimensional vector field
vecF=F_1hati+F_2hatj
is conservative if partial derivative
∂/(∂x)F_2−∂/(∂y)F_1=0
The LHS is also called
......................................
To determine whether a three dimensional vector field is conservative we find a function
Therefore if curl
Where curl