The potential field depends on the x - and y - coordinates as `V = x^2 - y^2`. The corresponding electric field lines in x y plane are as.

In a certain region of space, the potential field depends on x and y-coordinates as V=(-x^2+y^2) . The corresponding electric field lines in xy-plane are correctly represented by

Determine the electric field strength vector if the potential of this field depends upon x - and y - coordinates as : (i) V = a(x^2 - y^2) (ii) V = a x y .

Determine the electric field strength vector if the potential of this field depends on x, coordinates as (a) V = a (x^2 — y^2) (b) V = axy where, a is a constant.

The electric potential at any point x,y an z in metres is given by V = 3x^(2) . The electric field at a point (2,0,1) is

Gravitational potential in x-y plan varies with x and y coordinates as V = x^(2)y+2xy Find gravitational field strength E .

The potential at any point is given by V = x(y^2 - 4 x^2) . Calculate the cartesian components of the electric field at the point.

The electric field strength depends only on the x and y coordinates according to the law E = a (x i + yj) (x^(2) + y^(2)) , where a is a constant , i and j are the unit vectors of the x and y axes. Find the flux of the vector E through a sphere of raidus R with its centre at the origin of coordinates.

The electric field strength depends only on the x and y coordinates according to the law E = (a(xhati+ y hatj))/(x^(2) + y^(2)) , where a is a constant hati and hatj are unit vectors of the x and y axes . Find the potential difference between x = 1 and x = 5 :

The electirc potential at a point (x, y, z) is given by V = -x^(2)y - xz^(3) + 4 The electric field vecE at that point is