Magnetism and Gauss’s Law

Verify the Gauss’s law for magnetic field of a point dipole of dipole moment m at the origin for the surface which is a sphere of radius R.

The figure shows two fish tanks, each having ends of width 1 foot. Tank A is 3 feet long while tank B is 6 feet long. Both tanks are filled with 1 foot of water.

S_A = the magnitude of the force of the water on the end of tank A

S_B = the magnitude of the force of the water on the end of tank B

B_A = the magnitude of the force of the water on the bottom of tank A

B_B = the magnitude of the force of the water on the bottom of tank B. Using the notation given above, Which one of the following sets of equations below is correct for this situation?

The susceptibility of magnesium at 300 K is 1.2 × 10⁻⁵. At what temperature will the susceptibility increase to 1.8 × 10⁻⁵?

A short magnet produces a deflection of 30° when placed at certain distance in tanA position of magnetometer. If another short magnet of double the length and thrice the pole strength is placed at the same distance in tanB position of the magnetometer, the deflection produced will be:

A magnet is suspended horizontally in the earth's magnetic field. When it is displaced and then released it oscillates is a horizontal plane with a period T. If a piece of wood of same moment of inertia (about the axis of rotation) as the magnet is attached to the magnet, what would the new period of oscillation of the system become?

Consider the two idealized systems: (i) a parallel plate capacitor with large plates and small separation and (ii) a long solenoid of length L >> R, radius of cross-section. In (i) E is ideally treated as a constant between plates and zero outside. In (ii) magnetic field is constant inside the solenoid and zero outside. These idealised assumptions, however, contradict fundamental laws as below:

If the magnetic lines of force are shaped like arcs of concentric circles with their centre at point O in a certain section of a magnetic field ______.

In what way is Gauss's law in magnetism different from that used in electrostatics ? Explain briefly.