(a) Define magnetic line of force. (b) A wire of length 10 cm carrying a current of 4.0 A is placed between the poles of a powerful electromagnet of magneti...

(a) Magnetic line of force

A magnetic line of force is a line (curve) drawn in a magnetic field such that the tangent to it at any point gives the direction of the magnetic field at that point; equivalently, it is the path along which a free (isolated) north pole would move if placed in the field.

(b) Force on the current-carrying wire

Data: \( L = 10\,\text{cm} = 0.10\,\text{m} \), \( I = 4.0\,\text{A} \), \( B = 2.0\,\text{T} \). The force is \( F = BIL\sin\theta \).

(i) Wire parallel to the field (\( \theta = 0^\circ \))

\[ F = BIL\sin 0^\circ = 0\,\text{N} \]

(ii) Maximum force (\( \theta = 90^\circ \))

\[ F = BIL = 2.0 \times 4.0 \times 0.10 = 0.80\,\text{N} \]

(iii) Wire at \( 60^\circ \) to the field

\[ F = BIL\sin 60^\circ = 0.80 \times 0.866 = 0.69\,\text{N} \]

(c) Use of keepers

Bar magnets are stored in pairs, laid side by side with the north pole of one next to the south pole of the other, and short bars of soft iron (keepers) are placed across the two ends. The keepers become magnetized by induction, and together with the magnets they form a closed loop of magnetic flux. This keeps the molecular magnets (domains) aligned and prevents self-demagnetization, so the magnets retain their strength.

(d) True bearing

The compass reads N 10° W relative to magnetic north, and magnetic north itself lies N 15° W of true north (angle of declination). Since both deviations are to the west, they add:

\[ 10^\circ + 15^\circ = 25^\circ \text{ west of true north} \]

The true bearing of the place is N 25° W.