An electric field given by `2i+3yjN/C` pierces Gaussian cube of side `1m` placed at origin such that its three sides represents `x,y` and `z` axes. The net charge enclosed within the cube is `n varepsilon_(0)`. Find the value of `n`

An electric field given by vec(E) = 4hat(i) - (20 y^(2) + 2) hat(j) pierces a Gussian cube of side 1 m placed at origin such that its three sides represents x,y and z axes. The net charge enclosed within the cube is x xx 10^(-10)C , where is _____. (take in_(0) = 8.85 xx 10^(-12) N^(-1)m^(-2)C^(2) )

In the given electric field vecE=[(d+x)hati+E_(0)hatj]N//Ca hypothetical closed surface is taken as shown in figure. The total charge enclosed within the closed surface is Kepsilon_(0) . Then, find the value of k . ( a=2m , b=3m and c=2m )

An electric field given vecE= 4.0hati -3.0(y^(2) + 2.0)j pierces a Gaussian cube of edge length 2.0 m and positioned as shown in the figure. (The magnitude E is in newtons per coulomb and the position z is in meters.) what is the electric flux through the (a) top face, (b) bottom face, (c) left face , (b) bottom facem (c) left face, and (d) back face ? (e) what is the net electric flux through the cube ?

A cube of side 1 is placed in a uniform field E, where E= E hat(i) . The net electric flux through the cube is

Electric field in a region is given by vec(E)=-4xhat(i)+6yhat(j) . The charge enclosed in the cube of side 1 m oriented as shown in the diagram is given by alpha in_(0) . Find the value of alpha .

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

A solid insulating sphere of radius a carries a net positive charge 3Q , uniformly distributed throughout its volume. Concentric with this sphere is a conducting spherical shell with inner radius b and outer radius c and having a net charge -Q, as shown in figure a. Consider a spherical Gaussian surface of radius rgtc, the net charge enclosed by this surface is ............. b. The direction of the electric field rgtc is ............. c. The electric field at rgtc is ............... . d. The electric field in the region with radius r, which cgtrgtb, is ............... e. Consider a spherical Gaussian surface of radius r, where cgtrgtb , the net charge enclosed by this surface is ................ . f. Consider a spherical Gaussian surface of radius r, where bgtrgta , the net charge enclosed by this surface is ................. . g. The electric field in the region bgtrgta is ................ . h. Consider a spherical Gaussian surface of radius rlta . Find an expression for the net charge Q(r) enclosed by this surface as a function of r. Note that the charge inside the surface is less than 3Q. i. The electric field in the region rlta is ................. . j. The charge on the inner surface of the conducting shell is .......... . k. The charge on the outer surface of the conducting shell is .............. . l. Make a plot of the magnitude of the electric field versus r.

A uniform cube of mass M is floating on the surface of a liquid with three fourth of its volume immersed in the liquid (density of liquid is rho ). Now a cubical cavity is made inside the cube and the cavity is filled by a material having twice the density of the original cube. The minimum dimension (sides) of this cavity such that this cube is now completely immersed in the liquid is [(4M)/(nrho)]^(1/3) . Find the value of n

(a) Define electric flux. Write its SI units. (b) The electric field components due to a charge inside the cube of side 0.1 m are as shown : E_(x)=alpha x, where alpha=500N//C-m E_(y)=0, E_(z)=0 . Calculate (i) the flux through the cube, and (ii) the charge inside the cube.

(a) Define electric flux. Write its SI units. (b) The electric field components due to a charge inside the cube of side 0.1 m are as shown : E_(x)=alpha x, where alpha=500N//C-m E_(y)=0, E_(z)=0 . Calculate (i) the flux through the cube, and (ii) the charge inside the cube.