The intensity of an electric field depends only on the coordinates x and y as follows,
`E = (a(xhati +y hatj))/(x^(2)+y^(2))` where, a is constant and `hati` and `hatj` are the unit vectors of the x and y axes. Find the charges within a sphere of radius R with the centre at the origin.

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 :

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.

hati and hatj are unit vectors along x and y axis. What is the magnitude and direction of the vector hati + hatj ?

A force vecF=Ahati+Bhatj is applied to a point whose radius vector relative to the origin is vecr=ahati+bhatj , where a , b , A , B are constants and hati , hatj are unit vectors along the X and Y axes. Find the torque vectau and the arm l of the force vecF relative to the point O .

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]

If hati and hatj are unit vectors along X-and Y-axis respective, then what is the magnitude and direction of hati +hatj and hati - hatj ?

A particle projected from origin moves in x-y plane with a velocity vecv=3hati+6xhatj , where hati" and "hatj are the unit vectors along x and y axis. Find the equation of path followed by the particle :-