Describe the effect on the magnetic field around straight wires and solenoids of changing the magnitude and direction of the current

4.5.3 Magnetic Effect of a Current

Learning Objective

Describe how the magnetic field around a straight conductor and inside a solenoid changes when the magnitude or the direction of the current is altered, and explain simple classroom methods for visualising these changes.

1 Magnetic Field Around a Straight Conductor

1.1 Pattern and Direction

• The field consists of concentric circles centred on the wire.
• Direction is given by the right‑hand rule: point the thumb in the direction of conventional current (positive → negative); the curled fingers show the sense of the magnetic field lines.

1.2 Quantitative Relation

For a long, straight wire the magnetic field strength at a distance r from the centre of the wire is

\( B = \dfrac{\mu_{0} I}{2\pi r} \)

where \( \mu_{0}=4\pi \times 10^{-7}\,\text{T·m·A}^{-1} \) and \( I \) is the current.

1.3 Qualitative Variation of the Field

• With distance \(r\): \(B\) decreases inversely with distance (‑ \(1/r\)). The farther you move from the wire, the weaker the field.
• With current magnitude \(I\): \(B\) varies directly with the current (‑ \(B \propto I\)). Doubling the current doubles the field at any given point.

1.4 Effect of Changing the Current

• Increase \(I\) (same direction) – \(B\) increases proportionally; the sense of the circles is unchanged.
• Decrease \(I\) (same direction) – \(B\) decreases proportionally.
• Reverse the direction of \(I\) – The circular field lines reverse sense (clockwise ↔ anticlockwise) while the magnitude of \(B\) for a given \(|I|\) stays the same.
• \(I = 0\) – No magnetic field is produced.

1.5 Practical Visualisation (Compass or Iron‑Filings Test)

Aim: Observe how the field pattern changes when the current magnitude or direction is altered.

1. Connect a low‑voltage DC source (e.g., a 3 V battery) to a straight piece of insulated copper wire.
2. Place a sheet of paper over the wire and arrange a small compass at several positions around the wire, or sprinkle fine iron filings on the paper.
3. Switch the circuit on. The compass needle (or the filings) aligns tangentially to the circular field lines.
4. Increase the current using a variable resistor; the needle deflection becomes larger, showing a stronger field.
5. Reverse the battery connections; the needle now points in the opposite sense, confirming the reversal of field direction.
6. Switch the circuit off before moving the wire or the compasses for safety.

2 Magnetic Field Inside a Solenoid

2.1 Pattern and Direction

• Inside a long solenoid the field lines are nearly parallel, uniformly spaced, and run along the axis of the coil.
• Outside the solenoid the field is very weak and spreads out.
• Direction is given by the right‑hand rule: curl the fingers in the sense of the current around the turns; the thumb points toward the north pole (the direction of the internal field).

2.2 Quantitative Relation

For an ideal (long) solenoid the magnetic field inside is

\( B = \mu_{0} n I \)

where \( n \) is the number of turns per unit length (turns · m\(^{-1}\)). The field is essentially uniform across the cross‑section of the solenoid.

2.3 Qualitative Variation of the Field

• With current magnitude \(I\): \(B\) varies linearly (\(B \propto I\)).
• With turns per unit length \(n\): More tightly wound coils give a stronger field (\(B \propto n\)).
• With length of the solenoid: If the coil is not “long”, the field near the ends is weaker; the ideal formula assumes a length much greater than the diameter.

2.4 Effect of Changing the Current

• Increase \(I\) (same winding sense) – \(B\) inside increases linearly; the polarity (north/south) does not change.
• Decrease \(I\) (same winding sense) – \(B\) inside decreases linearly.
• Reverse \(I\) – The internal field reverses direction (north ↔ south) while the magnitude for a given \(|I|\) remains the same.
• \(I = 0\) – The internal field disappears.

2.5 Practical Visualisation (Compass Array)

Aim: Show the uniform field inside a solenoid and its reversal when the current direction is changed.

1. Wind ≈ 200 turns of insulated copper wire around a non‑magnetic tube (e.g., a PVC pipe) to form a solenoid.
2. Place a row of small compasses evenly spaced along the length of the tube, inside the coil.
3. Connect the coil to a low‑voltage DC supply through a switch.
4. Close the switch. All the compass needles align in the same direction, demonstrating the uniform internal field.
5. Reverse the supply connections; the needles all turn through 180°, showing that the field direction has reversed.
6. Switch the circuit off before repositioning any component.

3 Summary of the Effect of Changing Current

4 Key Points to Remember

1. The magnetic field around a straight conductor forms concentric circles; use the right‑hand rule to set the direction.
2. Field strength varies directly with current magnitude and inversely with distance from the wire (\(B \propto I/r\)).
3. Reversing the current reverses the field direction but does not change its magnitude.
4. Inside a long solenoid the field is uniform, parallel to the axis, and given by \(B = \mu_{0} n I\).
5. Increasing the current or the number of turns per unit length strengthens the solenoid field linearly; reversing the current swaps the north and south poles.
6. Simple classroom experiments with a compass (or iron filings) clearly demonstrate both the pattern of the field and the effect of changing current.