A hollow cylindrical box of length 0.5m and area of cross-section `20cm^(2)` is placed in a three dimensional coordinate system as shown in the figure. The electric field in the region is given by `vec E = 20 x hat i`, where E is `NC^(-1)` and x is in meters, Find

(i) Net flux through the cylinder.
(ii) Charge enclosed in the cylinder.

A bollow cylindrical box of length 1m and area of cross section 25 cm^(2) is placed in a three dimensional co-ordinate system as shown in Fig, The electric field in the region is given by vec(E) = 50 x hat(i) , where E is in NC^(-1) and x is in meter. Find (i) Net flux through the cylinder (ii) Charge enclosed by the cylinder.

The electric field in a region is given by E=ahati+bhatj . Hence as and b are constants. Find the net flux passing through a square area of side I parallel to y-z plane.

The electric field in a region is given by E=ahati+bhatj . Hence as and b are constants. Find the net flux passing through a square area of side I parallel to y-z plane.

A cube has sides of length L = 0.2 m. It is placed with one corner at the origin as shown in figure. The electric field is uniform and given by E= (2.5 N//C) hati - (4.2 N//C) hatj . Find the electric flux through the entire cube.

Electric field in a region is given by vec( E) = - 4xhat(i) + 6yhat(j) . Then find the charge enclosed in the cube of side 1m oriented as shown in the diagram

If electric field in the space is given by, vec E = 4x hati + (y^2+1)hatj and electric flux through ABCD is phi_1 and electric flux through BCEF is phi_2 , then find ( phi_1 - phi_2 )

(A)Two point charges q_1 and q_2 are kept r distance apart in a uniform external electric field vecE . Find the amount of work done in assembling this system of charges. (B) A cube of side 20 cm is kept in a region as shown in the figure. An electric field vecE exists in the region such that the potential at a point is given by V = 10x + 5 , where V is in volt and x is in m. Find the electric field vecE and (ii) total electric flux through the cube.

The electric field in a region is given by vecE=3/5 E_0veci+4/5E_0vecj with E_0=2.0 xx 10^3 N C^(-1) . Find the flux of this field through a recatngular surface of area 0.2m^2 parallel to the y-z plane.

The electric field in a region is given by E = 3/5 E_0hati +4/5E_0j with E_0 = 2.0 × 10^3 N//C . Find the flux of this field through a rectangular surface of area 0.2 m^2 parallel to the y-z plane.

State Gauss’s law in electrostatics. A cube with each side a is kept in an electric field given by E = Cx (as shown in the figure) where C is a positive dimensional constant. Find out : (i) The electric flux through the cube (ii) The net charge inside the cube.