(a) What is a magnetic field? (b) With the aid of a labelled diagram describe an experiment to show that a magnetic field exists around a straight wire carr...

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(a) A magnetic field is the region of space around a magnet or a current-carrying conductor within which a magnetic force is experienced by another magnet, a magnetic material, or a moving charge.

(b) Experiment to show that a magnetic field exists around a straight current-carrying wire (Oersted's experiment)

A stiff, straight copper wire is passed vertically through a hole in the centre of a horizontal cardboard sheet. The wire is connected in series with a battery, a switch (key) and a rheostat so that a large current can flow through it. Iron filings are sprinkled evenly over the card, and a small plotting compass is placed on the card near the wire.

When the switch is closed and a strong current flows, the card is gently tapped. The iron filings arrange themselves into a pattern of concentric circles centred on the wire, and the plotting compass needle sets itself tangential to these circles. This shows that a magnetic field exists in the space around the wire. When the direction of the current is reversed, the compass needle turns to point the opposite way, showing that the direction of the field also reverses.

(c) Series R-C circuit on a.c. supply: \(C = 40\,\mu\text{F} = 40\times10^{-6}\,\text{F}\), \(R = 40\,\Omega\), \(V = 100\,\text{V}\), \(f = 50\,\text{Hz}\).

(i) Circuit diagram — the 40 Ω resistor and the 40 µF capacitor connected in series across the 100 V, 50 Hz a.c. supply:

(ii) I. Impedance

Capacitive reactance:

\[ X_C = \frac{1}{2\pi f C} = \frac{1}{2\pi(50)(40\times10^{-6})} = 79.6\,\Omega \]

Impedance:

\[ Z = \sqrt{R^2 + X_C^2} = \sqrt{40^2 + 79.6^2} = \sqrt{1600 + 6337} = \sqrt{7937} = 89.1\,\Omega \]

II. Current in the circuit

\[ I = \frac{V}{Z} = \frac{100}{89.1} = 1.12\,\text{A} \]

III. Potential difference across the capacitor

\[ V_C = I\,X_C = 1.12 \times 79.6 = 89.2\,\text{V} \]