In Fig, electric field is directed along `+X` direction and is given by `E_(x) = 5 Ax + 2 B`, where E is in `NC^(-1)` and x is in meter, A and B are constants having dimensions. Taking `A = 10 NC^(-1) m^(-1) and B = 5 NC^(-1)`, calculate (i) the electric flux through the cube and (ii) net charge enclosed within the cube.

In Fig, electric field is dirceted along +X direction and is given by E_(x) = 5 Ax + 2 B , where E is in NC^(-1) and x is in meter, A and B are constants having dimenstions. Taking A = 10 NC^(-1) m^(-1) and B = 5 NC^(-1) , calculate (i) the electric flux through the cube and (ii) net charge enclosed within the cube.

If the electric field is given by vec(E) = 8 hat(i) + 4 hat(j) + 3 hat(k) NC^(-1) , calculate the electric flux through a surface of area 100 m^(2) lying in X-Y plane.

The electric field componets due to a charge inside the cube of side 0.1m are E_(x) = alpha x, where alpha = 500 (N//C) m^(-1) , E_(y) = 0, E_(z) = 0 . Calculate the flux through the cube and the charge inside the cube.

Using Gauss’s law, derive expression for intensity of electric field at any point near the infinitely long straight uniformly charged wire. The electric field components in the following figure are E_(x) = alphax, E_(y) = 0, E_(z) = 0, " in which " alpha = 400 N//C m. Calculate (i) the electric flux through the cube, and (ii) the charge within the cube assume that a = 0.1m.

Electric field at origin due to a point charge 1 nC placed at (1 ,1) m in x-y plane is