The electlric flux through a certain closed surface is zero i.e. `underset S oint vecE.vec(dS) = 0`. Does it necessarily imply that `vecE = 0`?

If underset s oint vecE.vec(ds)=0 over a surface, then

Electric field is the electrostatic force per unit charge acting on a vanishingly small test charge placed at that point. It is a vector quantity and the electric field inside a charged conductor is zero. Electric flux phi is the total number of electric lines of force passing through a surface in a direction normal to the surface when the surface is placed inside the electric field. phi=ointvecE.vec(ds)=q/epsilon_0 The electric field at a point is

Electric field is the electrostatic force per unit charge acting on a vanishingly small test charge placed at that point. It is a vector quantity and the electric field inside a charged conductor is zero. Electric flux phi is the total number of electric lines of force passing through a surface in a direction normal to the surface when the surface is placed inside the electric field. phi=ointvecE.vec(ds)=q/epsilon_0 If ointvecE.vec(ds)=0 over a surface, then

Electric field is the electrostatic force per unit charge acting on a vanishingly small test charge placed at that point. It is a vector quantity and the electric field inside a charged conductor is zero. Electric flux phi is the total number of electric lines of force passing through a surface in a direction normal to the surface when the surface is placed inside the electric field. phi=ointvecE.vec(ds)=q/epsilon_0 We have a Gaussian surface of radius R with Q at the centre, then

Electric field is the electrostatic force per unit charge acting on a vanishingly small test charge placed at that point. It is a vector quantity and the electric field inside a charged conductor is zero. Electric flux phi is the total number of electric lines of force passing through a surface in a direction normal to the surface when the surface is placed inside the electric field. phi=ointvecE.vec(ds)=q/epsilon_0 If there is only one type of charge in the universe, then

Electric field is the electrostatic force per unit charge acting on a vanishingly small test charge placed at that point. It is a vector quantity and the electric field inside a charged conductor is zero. Electric flux phi is the total number of electric lines of force passing through a surface in a direction normal to the surface when the surface is placed inside the electric field. phi=ointvecE.vec(ds)=q/epsilon_0 A positive charge Q is uniformly distributed along the circular ring of radius R. A small test charge q is placed at the centre of te ring as shown.

The magnetic flux phi (in weber) in a closed circuit of resistance 10 ohm varies with time t (in seconds) according to the equation : phi = 5t^2 - 4t +1 . At t = 0.2 s, the magnitude of the induced e.mf. In the circuit is

Careful measurement of the electric field at the surface of a black box indicates that the net outward flux through the surface of the box is 8.0 xx 10^3 Nm^2//C . If the net outward flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Why or Why not?

A current of 10 A is flowing in a long straight wire situated near a rectangular circuit whose two sides oflength 0.2m are parallel to the wire. One of them is at a distance of0.05m and the other at a distance of 0. IOm from the wire. The wire is in the plane of the rectangle. Find the magnetic flux through the rectangular circuit. If the current decays uniformly to zero in 0.02s, fmd the EMF induced in the circuit and indicate the direction in which the induced current flows.

Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where E = 0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable. Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.