A physics teacher explains Gauss's theorem in electrostatics and Gauss's theorem in magnetism to his students in a class. He tells them that total normal electric flux over a closed surface in vacuum is `phi_e=(Q)/(in_0)`, where Q is algebraic sum of charges inside the surface. Further, total normal magnetic flux over a closed surface in vacuum is always zero. The teacher emphasises that this is because in magnetism, poles always exist in unlike pairs of equal strengh, i.e., isolated magnetic poles called monopoles do not exist.
Read the above passage and answer the following questions:
(i) What are the implications of Gauss's theorem in magnetism in day to day life?
(ii) Two magnetic dipoles of moments `5Am^2` and `3Am^2` oriented along opposite directions are enclosed in a surface. What is total normal magnetic flux over this surface?
(iii) Two point charges `+4q` and `-q` are enclosed in a surface in vacuum, and third charge `5q` lies outside the surface. What is total normal electric flux over the surface?

Explanation

(i) In day to day life, we can visualize north pole of a magnetic dipole as source and south pole of the dipole as sink. When source and sink (of magnetic flux) having the same strength are enclosed by a surface, the total normal magnetic flux from the surface (i.e., net out come) will be zero. Hence, to achieve success in any sphere of life, we must identify the sinks and plug them property. Arrange to have as many sources as possible and success will be yours.
(ii) As stated in the theorem, total normal magnetic flux over the surface would always be zero, it being zero for every individual magnetic dipole.
(iii) `phi_e=(sumq_(i nside))/(in_0)=(4q-q)/(in_0)=(3q)/(in_0)`