$A$ compass needle is free to rotate in a horizontal plane. Its magnetic moment is $60 \ Am^2$. When it is pointing geographical north,it experiences a torque of $1.2 \times 10^{-3} \ Nm$ due to the Earth's magnetic field. If the Earth's magnetic field in the horizontal direction is $40 \times 10^{-6} \ T$,what is the declination in degrees at that place?

Lines which represent places of constant angle of dip are called

What is the dynamo effect?

Answer the following questions:
$(a)$ The earth's magnetic field varies from point to point in space. Does it also change with time? If so,on what time scale does it change appreciably?
$(b)$ The earth's core is known to contain iron. Yet geologists do not regard this as a source of the earth's magnetism. Why?
$(c)$ The charged currents in the outer conducting regions of the earth's core are thought to be responsible for earth's magnetism. What might be the 'battery' (i.e.,the source of energy) to sustain these currents?
$(d)$ The earth may have even reversed the direction of its field several times during its history of $4$ to $5$ billion years. How can geologists know about the earth's field in such distant past?
$(e)$ The earth's field departs from its dipole shape substantially at large distances (greater than about $30,000\; km$). What agencies may be responsible for this distortion?
$(f)$ Interstellar space has an extremely weak magnetic field of the order of $10^{-12}\; T$. Can such a weak field be of any significant consequence? Explain.

The true value of the angle of dip at a place is $60^o$. The apparent dip in a plane inclined at an angle of $30^o$ with the magnetic meridian is:

The angle of dip at a place is $40.6^\circ$ and the intensity of the vertical component of the earth's magnetic field $V = 6 \times 10^{-5} \text{ Tesla}$. The total intensity of the earth's magnetic field $(I)$ at this place is: