(a) Sketch the form of the magnetic flux pattern due to a current flowing (i) in a long solenoid (ii) through two long straight parallel wires when the dire...

(a) Magnetic flux patterns

(i) Long solenoid

The magnetic field is strong and nearly uniform inside the solenoid. Its pattern is like that of a bar magnet: field lines emerge from the north pole and return to the south pole outside the solenoid.

(ii) Two long parallel wires carrying currents in opposite directions

The magnetic fields are circular about each wire. In the region between the wires, the fields are in the same direction and reinforce; outside the wires, they oppose.

(b) Electric bell

When the switch is closed, current flows through the coils and magnetises the soft-iron cores of the electromagnet. The electromagnet attracts the soft-iron armature, causing the hammer to strike the gong.

As the armature moves towards the electromagnet, it moves away from the contact screw and breaks the circuit. The electromagnet then loses its magnetism. The spring pulls the armature back, restoring contact with the screw and completing the circuit again. This rapid make-and-break action continues while the switch is pressed, making the hammer strike the gong repeatedly.

(c) Calculations

For two cells in series:

\[E=2(1.5)=3.0\text{ V},\qquad r=2(1.0)=2.0\ \Omega\]

(i) If \(R\) is the effective resistance of the bell,

\[I=\frac{E}{R+r}\]

\[0.2=\frac{3.0}{R+2.0}\]

\[R+2.0=\frac{3.0}{0.2}=15\]

\[\boxed{R=13\ \Omega}\]

(ii) With the cells in parallel,

\[E=1.5\text{ V},\qquad r=\frac{1.0}{2}=0.5\ \Omega\]

\[I=\frac{E}{R+r}=\frac{1.5}{13+0.5}=\frac{1.5}{13.5}=0.111\ldots\text{ A}\]

\[\boxed{I\approx 0.11\text{ A}}\]