If $\theta_1$ and $\theta_2$ are the apparent angles of dip observed in two vertical planes at right angles to each other,then the true angle of dip $\theta$ is given by:

At a place,the magnitudes of the horizontal component and total intensity of the magnetic field of the earth are $0.3 \; Oersted$ and $0.6 \; Oersted$ respectively. The value of the angle of dip at this place will be.....$^o$

The horizontal component of the Earth's magnetic field is $0.22 \ G$ and the total magnetic field is $0.4 \ G$. The angle of dip is:

At a place,if the earth's horizontal and vertical components of magnetic fields are equal,then the angle of dip will be.......$^o$

The angle of dip at a certain place on earth is $60^{\circ}$ and the magnitude of earth's horizontal component of magnetic field is $0.26 \, G$. The magnetic field at the place on earth is.....$G$

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.