4.5.3 Magnetic Effect of a Current
Objective
- Describe a qualitative experiment that shows the pattern and direction of the magnetic field produced by:
- a straight current‑carrying wire, and
- a solenoid.
- Explain qualitatively how the field strength varies:
- with distance \$r\$ from a straight wire, and
- with position along and outside a solenoid.
- State how the field changes when the magnitude or direction of the current is altered.
Key Theory
For the IGCSE practical we treat the conductors as idealised.
- Long straight wire (idealised as infinite)
Magnetic field at a radial distance \$r\$:
\[
B = \frac{\mu_{0} I}{2\pi r}\qquad\left[\text{T}\right]
\]
where \(\mu_{0}=4\pi\times10^{-7}\,\text{N·A}^{-2}\), \(I\) is the current and \(r\) the distance from the wire.
→ \(B\propto I\) and \(B\propto \dfrac{1}{r}\).
- Ideal solenoid (length ≫ diameter, tightly wound)
Magnetic field inside the coil:
\[
B = \mu_{0} n I\qquad\left[\text{T}\right]
\]
with \(n\) = number of turns per metre (turns / length).
Inside the solenoid the field is essentially uniform and parallel to the axis; outside it rapidly falls to near‑zero.
→ \(B\propto I\) and \(B\propto n\).
Right‑hand rules (qualitative only)
- Straight wire – point the thumb in the direction of conventional current; the curled fingers give the direction of the magnetic field lines (concentric circles around the wire).
- Solenoid – grip the coil with the right hand so that the fingers follow the direction of the windings; the thumb points in the direction of the magnetic field inside the solenoid.
Simple ASCII view (side of the wire):
Current → (thumb)
B‑field direction (fingers) → ⟳ ⟳ ⟳
Apparatus
| Item | Purpose |
|---|
| Low‑voltage DC supply (≤ 12 V) or 2 × 1.5 V cells | Provides a steady, adjustable current. |
| Ammeter (0–5 A range) | Measures the current flowing through the circuit. |
| Straight insulated copper wire (≈ 1 m, bare ends) | Source of a magnetic field for the wire experiment. |
| Solenoid (≈ 200 turns, length 10 cm, diameter 2 cm) | Creates a nearly uniform magnetic field inside. |
| Connecting leads with crocodile clips | Complete the circuit safely. |
| Compass (or a set of small magnetic needles on a pivot) | Detects the direction of the magnetic field (qualitative only). |
| Ruler or measuring tape | Set accurate distances from the wire/solenoid. |
| Plain sheet of paper and pencil | Record needle orientations and sketch field lines. |
Safety Considerations
- Use low voltage and keep current below 3 A to avoid overheating.
- Do not touch the wire or leads while the circuit is powered.
- Switch off the supply before changing connections or moving the compass.
- Keep the compass away from strong permanent magnets.
- Secure all apparatus on a stable, non‑magnetic surface.
Experimental Procedure
1. Straight wire
- Connect the straight wire, ammeter and power supply as shown in the diagram (wire → ammeter → supply → back to wire). Verify the ammeter reads zero before switching on.
- Lay a sheet of paper on a flat surface. Mark three positions at distances \(r =\) 2 cm, 5 cm and 10 cm from the wire (measure from the centre of the wire).
- Place the compass at a chosen distance, note the needle direction with the current OFF (this is the Earth’s field direction). Mark the centre of the compass with a pencil dot.
- Switch the supply ON and adjust the current to a moderate value (e.g., 1 A). Record the new needle direction.
- Repeat step 4 for a second current (e.g., 2 A) keeping the distance constant.
- Reverse the current direction (swap the supply leads) and repeat steps 3–5. Observe the opposite sense of needle rotation.
- Repeat the whole set of measurements for each of the three distances.
2. Solenoid
- Replace the straight wire with the solenoid, keeping the same ammeter‑supply arrangement.
- Insert the compass into the centre of the coil (along the axis) and note the needle direction with the current OFF.
- Switch the current ON (use the same two current values as for the wire) and record the needle orientation.
- Move the compass to a point just outside each end of the solenoid and repeat step 3 for both currents.
- Reverse the current direction and repeat steps 2–4.
Typical Observations
| Setup | Current (A) | Distance / Position | Compass deflection (° from geographic north) | Interpretation |
|---|
| Straight wire – left of wire | +1 (into page) | 2 cm | ≈ +45° (clockwise) | Field circles wire – right‑hand rule. |
| Straight wire – left of wire | +2 | 2 cm | ≈ +90° | Deflection roughly doubles → \(B\propto I\). |
| Straight wire – right of wire | +1 | 5 cm | ≈ ‑30° (anticlockwise) | Opposite sense on opposite side; smaller angle → \(B\propto 1/r\). |
| Solenoid – centre (axis) | +1 (clockwise when viewed from left) | inside | Needle aligns with axis, pointing left→right. | Uniform field inside; direction given by right‑hand grip rule. |
| Solenoid – centre (axis) | +2 | inside | Needle aligns more sharply (larger torque). | Torque ∝ \(B\propto I\) (and ∝ \(n\)). |
| Solenoid – just outside end | +1 | outside | ≈ 5° | External field is weak; lines loop back. |
Analysis
- Pattern for a straight wire – The compass needle turns in opposite directions on opposite sides of the wire, confirming that the magnetic field consists of concentric circles centred on the conductor. The sense follows the right‑hand rule.
- Field‑strength variation (straight wire) – For a fixed current the deflection angle decreases as the distance \$r\$ increases, consistent with \(B\propto 1/r\). Doubling the current roughly doubles the deflection, showing \(B\propto I\).
- Pattern for a solenoid – Inside the coil the needle aligns with the axis, indicating a uniform field parallel to the length. Outside the coil the needle shows only a small deflection, illustrating that the field there is weak and loops back.
- Field‑strength variation (solenoid) – Along the central region the needle orientation is essentially the same at different axial positions, confirming that \(B\) is approximately constant (independent of position). Near the ends the field drops sharply, matching the expectation that the ideal formula \(B=\mu_{0}nI\) applies well only away from the ends.
- Effect of changing the current – In both experiments the direction of the needle reverses when the current direction is reversed, and the magnitude of the deflection (hence the field) scales linearly with the current (doubling \(I\) roughly doubles \(B\)).
- Role of the turn density \(n\) – For the solenoid, increasing the number of turns per metre (e.g., using a longer coil with the same total turns) would increase the field proportionally, as shown by the factor \(n\) in \(B=\mu_{0}nI\).
Evaluation (AO3)
Possible sources of error
- Friction in the compass pivot creates a small “dead‑zone” before the needle moves.
- Earth’s magnetic field adds a constant background; if not subtracted, it slightly skews measured angles.
- The wire is not truly infinite; end effects become noticeable when the observation point is a sizable fraction of the wire length away.
- Current may fluctuate during the measurement, giving an uncertain \(I\) value.
- Heating of the wire changes its resistance, causing a gradual drift in current.
Improvements
- Use a longer straight wire (≥ 2 m) to minimise end effects.
- Replace the compass with a calibrated gauss‑meter or Hall probe for quantitative field values.
- Take three readings at each setting and use the average to reduce random error.
- Carry out the experiment on a non‑magnetic table and keep other metallic objects away to avoid stray fields.
- Record the exact current from the ammeter each time and note any temperature rise of the wire.
Conclusion
The practical investigation confirms the textbook patterns of magnetic fields produced by currents:
- Straight conductor – magnetic field lines are circular, centred on the wire; direction follows the right‑hand rule; field strength falls off as \(1/r\) and is directly proportional to the current.
- Solenoid – inside the coil the field is uniform, parallel to the axis, and its magnitude is given by \(B=\mu_{0}nI\); outside the field is weak and loops back. Reversing the current reverses the field direction in both cases.
These qualitative observations provide the experimental basis required by the Cambridge IGCSE for using right‑hand rules to predict magnetic‑field directions in a wide range of electromagnetic applications.