State Lenz's law. Illustrate, by giving an example, how this law helps in predicting the direction of the current in a loop in the presence of a changing magnetic flux.

In a given coil of self-inductance of 5 mH, current changes from 4 A to 1 A in 30 ms. Calculate the emf induced in the coil.

                                                                 OR

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

The Earth's magnetic field at the Equator is approximately 0.4 G. Estimate the Earth's magnetic dipole moment. Given: Radius of the Earth = 6400 km. 

Lenz law states that,polarity of the induced emf is such that it opposes a change in magnetic flux.

The given activity demonstrates the above statement. The amount of magnetic flux linked with the coil increases, when the north pole of a bar magnet is brought near the coil. Current in the coil is induced in a so as to opposes the increase in magnetic flux. This is possible only when the current induced in the coil is in anti-clockwise direction, with respect to an observer. The magnetic moment  associated with this induced emf has north polarity, towards the north pole of the approaching bar magnet.

Similarly, magnetic flux linked with the coil decreases when the north pole of the bar magnet is moved away from the coil. Inorder to oppose this decrease in magnetic flux, current is induced in the coil in clockwise direction so that its south pole faces the receding north pole of the bar magnet. This would result in an attractive force which opposes the motion of the magnet and the corresponding decrease in magnetic flux.

Given,

Self-inductance, L = 5 mH = 510^-3 H

Change in current, dI = (4-1) = 3 A

Change in time, dt = 30 ms = 3010^-3 s
So, emf induced in the coil is given by, 
 

                                                             OR

i) Gauss’s law for magnetism states that magnetic flux through any closed surface is 0.

That is, 
                            
Gauss law for electrostatics states that electric flux through a closed surface is give n by,
                             

Therefore, electric flux is zero when the surface encloses an electric dipole.

Magnetic flux is zero implies that, isolated magnetic poles do not exist.

ii) Given,

Magnetic field of Earth = 0.4 G = 0.4 10^-4 G

Equatorial magnetic field of earth is given by, 

where, d = 6400km = 6.4 x 10⁶ m

Therefore, Earth’s magnetic dipole moment is given by,