Find the potential `varphi (x,y)` of an electrostatic field `E = 2axyi + a (x^(4) - y^(2)) j`, where `a` is a constant, `I` and `J` are the unit vectors of the `x` and `y` axes.

Find the potential function V (x,y) of an electrostatic field vec(E)=2axy hat(i)+a(x^(2)-y^(2))hat(j) where a is a constant.

Find the potential function V (x,y) of an electrostatic field vec(E)=2axy hat(i)+a(x^(2)-y^(2))hat(j) where a is a constant.

Determine the potentail varphi(x,y,z) of an electrostatic field E = ayl + (ax + bz) J + byk , where a and b are constants, I, j, k are the unit vectors of the axes x,y,z .

Determine the potential phi (x,y,z) of an electrostatic field vec(E) = ay hati + (ax + bz) hatj + by hatk , where a and b are constants, hati, hatj are the unit vectors of the axes x,y,z. [-y(ax +bz)+ constant]

Find the potential V of an electrostatic field vec E = a(y hat i + x hat j) , where a is a constant.

Find the potential V of an electrostatic field vec E = a(y hat i + x hat j) , where a is a constant.

The potential phi(x,y) of an electrostatic field E=a(y hat(i)+c hat(j)) is [ a is a constant and hat(i) and hat(j) are unit vectors along X and Y axes ]

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.

In an interial reference frame K there is only magnetic field with induction B = b (yl -x)//(x^(2) + y^(2)) , where b is a constane, i and j are the unit vectors of the x and y axes. Find the elecric field strength E' in the frame K' moving relative to the frame K with a constatn non-relative velocity v = vk, k is the unit vector of the z-axis. The z' axis is assumed to coincule with the z axis. What is the shape of the field E' ?