Magnetic Fields Due to Currents (Syllabus 9702: 20.4)

Hello future physicist! This chapter is where electricity meets magnetism, a beautiful partnership known as electromagnetism. Don't worry if this sounds complicated—we are just going to explore the invisible fields created whenever charge moves (i.e., whenever there is a current). Understanding these fields is essential for everything from electric motors to large accelerators!

What You Will Learn Here:

  • How to draw and visualize magnetic fields around wires and coils.
  • How to use simple rules (like the Right Hand Grip Rule) to find the direction of these fields.
  • Why current-carrying wires exert forces on each other.

1. Magnetic Field Patterns and Direction

The crucial starting point is understanding that moving charge produces a magnetic field. The shape and direction of this field depend entirely on the shape of the conductor carrying the current.

1.1 The Long Straight Wire

When current flows through a long, straight conductor (like a simple wire), the magnetic field produced forms concentric circles around the wire.

  • The field lines are centered on the wire.
  • The lines are closest together near the wire, meaning the magnetic field strength (magnetic flux density, B) is greatest close to the current and decreases as you move further away.

How to find the direction? Use the Right-Hand Grip Rule (RHGR)!

  1. Imagine gripping the wire with your right hand.
  2. Point your right thumb in the direction of the conventional current (positive to negative).
  3. Your curled fingers show the direction of the magnetic field lines.

Analogy: Think of opening a bottle cap. If your thumb points up (current), your fingers curl in the direction you would twist the cap (field).

Quick Review: For a straight wire, the field is a series of concentric circles, and its direction is given by the Right-Hand Grip Rule.

2. Fields Produced by Coils and Solenoids

When you bend a straight wire into a loop or a spring, the shape of the resulting magnetic field changes dramatically, and it begins to resemble the field of a traditional bar magnet.

2.1 The Flat Circular Coil (Loop)

If you take a straight wire and bend it into a single loop (a flat circular coil):

  • Near the edges of the loop, the field lines are circular, following the RHGR.
  • At the very centre of the loop, the magnetic field lines become straight, uniform, and perpendicular to the plane of the coil.
2.2 The Long Solenoid

A solenoid is essentially a long coil of wire wrapped tightly in the shape of a cylinder (like a spring). When current passes through it, it creates a powerful and useful magnetic field.

  • Outside the solenoid: The field pattern is identical to that of a bar magnet, showing distinct North and South poles at the ends.
  • Inside the solenoid: The field is very strong and highly uniform (constant strength and direction). This uniform field is often used in physics experiments and applications.

Determining Solenoid Polarity (N/S):
You can use a modified Right-Hand Grip Rule here:

  1. Wrap your right fingers in the direction of the current flowing through the loops of the solenoid.
  2. Your right thumb will point towards the North Pole of the solenoid.
2.3 Increasing Solenoid Field Strength (The Ferrous Core)

The syllabus requires you to understand how the magnetic field in a solenoid is increased by a ferrous core.

A ferrous core (made of soft iron or steel, which are ferromagnetic materials) is placed inside the solenoid. These materials have tiny regions called domains, which are like tiny internal magnets.

  1. When the solenoid current creates a field, these domains align themselves strongly with this external field.
  2. This alignment creates a massive internal magnetic field within the core.
  3. This self-generated field from the core adds to the field produced by the coils, leading to a dramatically increased total magnetic field (up to thousands of times stronger).

Did you know? This is the fundamental principle behind electromagnets—they allow us to switch huge lifting forces on and off simply by controlling the current in a coil.

Key Takeaway: Coils and solenoids produce fields similar to bar magnets. A ferrous core concentrates and amplifies this field significantly.

3. Forces Between Current-Carrying Conductors

Now we combine concepts. If Wire A carries a current, it creates a magnetic field. If Wire B carries a current and is placed within Wire A's magnetic field, Wire B must experience a force (since a moving charge experiences a force in a magnetic field, as covered in 20.2/20.3).

3.1 The Origin of the Force (Syllabus 20.4.3)

The forces between two parallel current-carrying wires are a direct result of the principle of electromagnetism:

  • Current 1 creates Magnetic Field 1.
  • Current 2 experiences a force because it is cutting through Magnetic Field 1.
  • Simultaneously, Current 2 creates Magnetic Field 2, and Current 1 experiences an equal and opposite force because it is cutting through Magnetic Field 2 (Newton’s Third Law).
3.2 Determining the Direction of the Force

To find the direction of the force (F), we use Fleming's Left-Hand Rule (FLHR). This rule relates the direction of the field (B), the direction of the current (I), and the resulting force (F).

  • Forward (Thumb): Direction of the Force (Motion).
  • Big finger (Index Finger): Direction of the B-Field (North to South).
  • Interior finger (Middle Finger): Direction of the I (conventional Current).

Step-by-Step for Two Parallel Wires:

  1. Step 1: Find Field 1. Use RHGR to determine the direction of the field created by Wire 1 at the position of Wire 2.
  2. Step 2: Find Force 2. Use FLHR, pointing the index finger (B) in the direction found in Step 1, and the middle finger (I) in the direction of the current in Wire 2.
  3. Step 3: The Result. The thumb (F) gives the direction of the force on Wire 2.

The Two Main Results (Memorize this!)

  1. Parallel Currents (currents flowing in the same direction):

    If Current 1 is Up and Current 2 is Up, the wires ATTRACT each other.

  2. Anti-parallel Currents (currents flowing in opposite directions):

    If Current 1 is Up and Current 2 is Down, the wires REPEL each other.

Memory Aid: Think of people walking the same way (parallel) - they stick together (attract). People fighting (opposite direction) - they push each other away (repel).

Common Mistake to Avoid!

Students often mix up the two rules. Remember: RHGR is ONLY for finding the direction of the B-field created by a current (Cause). FLHR is ONLY for finding the direction of the Force exerted on a current (Effect).

Quick Chapter Summary (Checklist)

  • Straight Wire Field: Concentric circles. Direction found using Right-Hand Grip Rule (Thumb = I, Fingers = B).
  • Solenoid Field: Acts like a bar magnet externally, is uniform and strong internally.
  • Ferrous Core: Increases the solenoid field strength significantly because the core material aligns its magnetic domains.
  • Force Between Wires: Caused by the magnetic field of one wire interacting with the current of the other.
  • Direction of Force: Found using Fleming's Left-Hand Rule (F-B-I).
  • Attraction/Repulsion: Parallel currents attract; anti-parallel (opposite) currents repel.

Great job tackling Magnetic Fields! These rules are fundamental and will be used again when we study motors and induction. Keep practicing those hand rules until they become second nature!