CIE AS/A Level Physics 20.4 Magnetic fields due to currents Study Notes- 2025-2027 Syllabus
CIE AS/A Level Physics 20.4 Magnetic fields due to currents Study Notes – New Syllabus
CIE AS/A Level Physics 20.4 Magnetic fields due to currents Study Notes at IITian Academy focus on specific topic and type of questions asked in actual exam. Study Notes focus on AS/A Level Physics latest syllabus with Candidates should be able to:
- sketch magnetic field patterns due to the currents in a long straight wire, a flat circular coil and a long solenoid
- understand that the magnetic field due to the current in a solenoid is increased by a ferrous core
- explain the origin of the forces between current-carrying conductors and determine the direction of the forces
Magnetic Field Patterns for Different Current-Carrying Conductors
Current-carrying conductors produce characteristic magnetic field patterns. These patterns can be visualised using field lines (lines of magnetic flux). The direction of the field is given by the right-hand rule:
Thumb → direction of current Fingers curl → direction of magnetic field
1. Magnetic Field of a Long Straight Wire
- Field lines are concentric circles around the wire.
- Spacing increases with distance → field strength decreases with distance.
- Direction found using right-hand rule.
Sketch Features:
- Wire drawn vertically or horizontally.
- Circular field lines centered on wire.
- Arrows on circles showing direction (clockwise or anticlockwise).
2. Magnetic Field of a Flat Circular Coil
- Field lines loop through the centre of the coil.
- At the centre: field is strong and almost uniform.
- Direction given by right-hand rule: curl fingers around coil → thumb gives direction of field through centre.
Sketch Features:
- Coil drawn as a circle.
- Field lines emerging from one side and entering the other (like a small bar magnet).
- Inside coil: straight, parallel lines.
3. Magnetic Field of a Long Solenoid
- Inside the solenoid → strong, uniform magnetic field with parallel and equally spaced lines.
- Outside the solenoid → weak field resembling a bar magnet.
- Polarity decided by right-hand grip rule (curl in direction of current → thumb gives North pole).
Sketch Features:
- Long cylinder shape with coil windings.
- Inside → straight, parallel field lines.
- Outside → curved lines looping around.
Example
Describe how you would sketch the magnetic field around a straight current-carrying wire.
▶️ Answer / Explanation
- Draw the wire as a straight line.
- Draw concentric circles around it to represent field lines.
- Use arrows to show direction given by right-hand rule.
- Show closer spacing near wire and wider spacing further out.
Example
Explain how the magnetic field pattern at the centre of a flat circular coil differs from the field pattern far from the coil.
▶️ Answer / Explanation
At the centre:
- Field lines are almost straight and parallel → nearly uniform field.
- Field strength is maximum.
Far from the coil:
- Field lines spread out and curve.
- Field becomes weak and non-uniform.
Example
A solenoid carries a steady current. Describe how to sketch the magnetic field inside and outside the solenoid, and explain why the field is uniform inside.
▶️ Answer / Explanation
Sketch description:
- Draw the solenoid as a long cylinder with several turns.
- Inside → draw parallel, equally spaced lines showing strong, uniform field.
- Outside → draw curved, weakening field lines resembling a bar magnet.
Reason for uniform field:
- The magnetic fields from each turn of the coil overlap and reinforce each other.
- In the central region, the contributions add to form straight, equally spaced lines.
- Edge effects are negligible for a long solenoid.
Result: a strong, uniform magnetic field inside.
Magnetic Field in a Solenoid with a Ferrous Core
A solenoid produces a magnetic field when a current flows through it. The strength of this magnetic field can be greatly increased by inserting a ferrous core (such as iron) into the solenoid.
Why a Ferrous Core Increases the Magnetic Field
- Ferrous materials (iron, steel, nickel) have a very high magnetic permeability.
- They contain many tiny magnetic domains.
- These domains align strongly with the solenoid’s magnetic field.
- The aligned domains produce their own magnetic field that adds to the solenoid’s field.
- This results in a much stronger total magnetic field inside and around the solenoid.
Effect on the Solenoid:
- Magnetic field becomes much stronger → sometimes hundreds of times larger.
- Field lines become denser and more concentrated inside the core.
- Solenoid effectively becomes an electromagnet.
Why Ferrous Cores Are Used:
- To create strong electromagnets (cranes, motors, speakers).
- To improve efficiency of inductors and transformers.
- To concentrate magnetic fields in magnetic circuits.
Example
A solenoid is switched on without a core, and then a soft iron rod is inserted. What happens to the magnetic field strength inside the solenoid?
▶️ Answer / Explanation
Soft iron has high magnetic permeability, so its domains align with the solenoid’s field. This produces an additional magnetic field inside the solenoid.
The total magnetic field becomes much stronger.
Example
Explain why the magnetic field inside a solenoid with an iron core is stronger than the field inside a solenoid with an air core, even when the current is the same.
▶️ Answer / Explanation
- Air has low magnetic permeability → hardly enhances the field.
- Iron has very high permeability → enhances the magnetic field strongly.
- Magnetic domains in iron align with the solenoid’s field.
- The aligned domains create their own field, which adds to the solenoid’s.
Thus the field inside the solenoid becomes significantly stronger with an iron core.
Example
A solenoid with no core produces a magnetic flux density of \( \mathrm{4.0\times10^{-3}\ T} \). When a ferrous core is inserted, the flux density becomes \( \mathrm{3.6\times10^{-2}\ T} \). Calculate the factor by which the field is increased, and explain why this occurs.
▶️ Answer / Explanation
Factor increase:
\( \mathrm{\dfrac{3.6\times10^{-2}}{4.0\times10^{-3}} = 9} \)
The field is increased by a factor of 9.
Explanation:
- The ferrous core has high magnetic permeability.
- Its internal domains align with the solenoid’s field.
- This alignment produces an additional magnetic field.
- Total field = solenoid field + field from aligned domains.
Therefore, the magnetic field becomes much stronger when a ferrous core is inserted.
Forces Between Current-Carrying Conductors
Two parallel current-carrying conductors exert forces on each other because each wire produces a magnetic field, and the other wire (carrying current) experiences a force due to that field.
Origin of the Force
- A current in a wire produces a magnetic field around it (concentric circles).
- The second wire lies within this magnetic field, so its moving charges experience a magnetic force:
\( \mathrm{F = B I L} \)
- The force on each wire depends on the direction of current in the other wire.
- The two forces form a Newton’s third law pair → equal in magnitude, opposite in direction.
Direction of Forces
Use the right-hand grip rule to find the field produced by one wire, then apply the left-hand rule to find the force on the other wire.
- Currents in the same direction → wires attract.
- Currents in opposite directions → wires repel.
Why?
- Same direction currents produce magnetic fields that align between the wires → lower magnetic energy → attraction.
- Opposite currents produce magnetic fields that oppose between the wires → higher magnetic energy → repulsion.
Steps to Determine the Direction of Force
- Use right-hand rule for wire 1 → find magnetic field direction at wire 2.
- Use Fleming’s left-hand rule on wire 2 to get the force on it.
- Repeat for wire 1 to confirm opposite force direction.
Example
Two long parallel wires carry currents in the same direction. What type of force acts between them?
▶️ Answer / Explanation
Currents in the same direction → magnetic fields reinforce between wires → lower field energy.
Thus, the wires attract.
Example
Wire A carries current upwards. Wire B, placed parallel to A, carries current downwards. Will they attract or repel, and why?
▶️ Answer / Explanation
- Currents are in opposite directions.
- Magnetic fields between the wires oppose each other → high magnetic energy region.
- System reduces energy by pushing wires apart.
The wires repel.
Example
Two long parallel wires are 6 cm apart. Wire 1 carries a current of 8 A upward. Wire 2 carries a current of 12 A also upward. Determine whether the wires attract or repel and explain the direction of the force on each wire.
▶️ Answer / Explanation
Step 1: Current direction
Both currents upward → same direction → attraction.
Step 2: Direction of force on Wire 2
- Use right-hand rule on Wire 1 → find its field direction at Wire 2.
- Use left-hand rule on Wire 2 → force points toward Wire 1.
Step 3: Force on Wire 1
- Equal and opposite → Wire 1 is pulled toward Wire 2.
Final Answer: The wires attract. Wire 2 is pulled toward Wire 1, and Wire 1 is pulled toward Wire 2.