Gausss Law Physics - Gausss Law

An electric dipole is placed at the centre of a sphere.
Mark the correct options:

1. The flux of the electric field through the sphere is zero.
2. The electric field is zero at every point of the sphere.
3. The electric field is not zero anywhere on the sphere.
4. The electric field is zero on a circle on the sphere.

A positive point charge Q is brought near an isolated metal cube.

1. The cube becomes negatively charged.
2. The cube becomes positively charged.
3. The interior becomes positively charged and the surface becomes negatively charged.
4. The interior remains charge free and the surface gets nonuniform charge distribution.

Figure shows a closed surface which intersects a conducting sphere. If a positive charged is placed at the point P, the flux of the electic field through the closed surface:

1. Will remain zero.
2. Will become positive.
3. Will become neagative.
4. Will become undefined.

Consider the situation of the previous problem. The force on the central charge due to the shell is:

1. Towards left.
2. Towards right.
3. Upward.
4. Zero.

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?

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?

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

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 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).

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 spherical volume contains a uniformly distributed charge of density 2.0 × 10^-4Cm^-3. Find the electric field at a point inside the volume at a distance 4.0cm from the centre.

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 charge Q is placed at the centre of an uncharged, hollow metallic sphere of radius a:

1. Find the surface charge density on the inner surface and on the outer surface.
2. If a charge q is put on the sphere, what would be the surface charge densities on the inner and the outer surfaces?
3. Find the electric field inside the sphere at a distance x from the centre in the situations (a) and (b).

Consider the situation of the previous problem:

1. Find the tension in the string in equilibrium.
2. Suppose the ball is slightly pushed aside and released. Find the time period of the small oscillations.

A long cylindrical wire carries a positive charge of linear density 2.0 × 10^-8Cm^-1. An electron revolves around it in a circular path under the influence of the attractive electrostatic force. Find the kinetic energy of the electron. Note that it is independent of the radius.

Two large conducting plates are placed parallel to each other with a separation of 2.00cm between them. An electron starting from rest near one of the plates reaches the other plate in 2.00 microseconds. Find the surface charge density on the inner surfaces.