Gausss Law Physics - Gausss Law

Find the flux of the electric field through a spherical surface of radius R due to a charge of 10^-7C at the centre and another equal charge at a point 2R away from the centre.

A charge Q is placed at the centre of a cube. Find the flux of the electric field through the six surfaces of the cube.

A charge Q is placed at the centre of an imaginary hemispherical surface. Using symmetry arguments and the Gauss's law, find the flux of the electric field due to this charge through the surface of the hemisphere (figure).

Show that there can be no net charge in a region m which the electric field is uniform at all points.

Three identical metal plates with large surface areas are kept parallel to each other as shown in figure. The leftmost plate is given a charge Q, the rightmost a charge -2Q and the middle one remains neutral. Find the charge appearing on the outer surface of the rightmost plate.

A charge Q is uniformly distributed over a rod of length l. Consider a hypothetical cube of edge l with the centre of the cube at one end of the rod. Find the minimum possible flux of the electric field through the entire surface of the cube.

A charged particle having a charge of -2.0 × 10^-6C is placed close to a nonconducting plate having a surface charge density 4.0 × 10^-5Cm^-2. Find the force of attraction between the particle and the plate.

A circular ring of radius r made of a nonconducting material is placed with its axis parallel to a uniform electric field. The ring is rotated about a diameter through 180°. Does the flux of electric field change? If yes, does it decrease or increase?

A rubber balloon is given a charge Q distributed uniformly over its surface. Is the field inside the balloon zero everywhere if the balloon does not have a spherical surface?

A point charge q is placed in a cavity in a metal block. If a charge Q is brought outside the metal, will the charge q feel an electric force?

If flux of the electric field through a closed surface is zero:

1. The electric field must be zero everywhere on the surface.
2. The electric field may be zero everywhere in the surface.
3. The charge inside the surface must be zero.
4. The charge in the vicinity of the surface must be zero.

Electric charges are distributed in a small volume. The flux of the electric field through a spherical surface of radius 10cm surrounding the total charge is 25V-m. The flux over a concentric sphere of radius 20cm will be:

1. 25V-m
2. 50V-m
3. 100V-m
4. 200V-m

Figure shows a charge q placed at the centre of a hemisphere. A second charge Q is placed at one of the positions A, B, C and D. In which position(s) of this second charge, the flux of the electric field through the hemisphere remains unchanged?

1. A
2. B
3. C
4. D

A closed surface S is constructed around a conducting wire connected to a battery and a switch (figure). As the switch is closed, the free electrons in the wire start moving along the wire. In any time interval, the number of electrons entering the closed surface S is equal to the number of electrons leaving it. On closing the switch, the flux of the electric field through the closed surface:

1. Is increased.
2. Is decreased.
3. Remains unchanged.
4. Remains zero.

A metallic particle having no net charge is placed near a finite metal plate carrying a positive charge. The electric force on the particle will be:

1. Towards the plate.
2. Away from the plate.
3. Parallel to the plate.
4. Zero.

One end of a 10cm long silk thread is fixed to a large vertical surface of a charged nonconducting plate and the other end is fastened to a small ball having a mass of 10g and a charge of 4.0 × 10^-5C. In equilibrium, the thread makes an angle of 60° with the vertical. Find the surface charge density on the plate.

Consider the following very rough model of a beryllium atom. The nucleus has four protons and four neutrons confined to a small volume of radius 10^-15m. The two 1s electrons make a spherical charge cloud at an average distance of 1.3 × 10^-11m from the nucleus, whereas the two 2s electrons make another spherical cloud at an average distance of 5.2 × 10^-11m from the nucleus. Find the electric field at:

1. A point just inside the 1s cloud.
2. A point just inside the 2s cloud.

Two conducting plates X and Y, each having large surface area A (on one side), are placed parallel to each other as shown in figure. The plate X is given a charge Q whereas the other is neutral. Find:

1. The surface charge density at the inner surface of the plate X.
2. The electric field at a point to the left of the plates.
3. The electric field at a point in between the plates.
4. The electric field at a point to the right of the plates.

Find the magnitude of the electric field at a point 4cm away from a line charge of density 2 × 10^-6Cm^-1.