Magnetic Fields Graphs

Magnetic field graphs show how the strength and direction of a magnetic field change with distance, position, or current. The vertical axis is usually magnetic field strength B (in tesla, T), and the horizontal axis is distance r, position along a line, or current I. A positive value can mean “field in the chosen reference direction”; a negative value means “opposite direction”.

Key ideas to read any graph

• Closer points with larger B mean a stronger field (like denser field lines).
• A horizontal (flat) line means a uniform field in that region.
• Curves that approach, but never touch, the axis show a field that gets weaker but does not suddenly become zero.

Typical graphs you should recognise

1) Straight current-carrying wire: B vs distance r

The field is strongest near the wire and decreases as you move away. The graph starts high at small r and curves down, never reaching zero. Qualitatively: $B \propto \tfrac{1}{r}$. Reversing the current flips the direction (the graph’s sign), not the shape.

2) Solenoid (long coil): B along its axis

• Inside (central region): nearly uniform field → a flat line at a positive value.
• Near the ends: the line falls (fringing).
• Outside: small values near zero.

If you plot B against current I for a given solenoid, the line is straight through the origin: $B \propto I$.

3) Bar magnet: B vs distance from a pole

The field is strongest close to a pole and drops quickly with distance. The curve falls steeply at first. Direction depends on which pole you face.

Common misconceptions

• Field lines are not objects; their spacing represents strength.
• The field does not stop suddenly; it fades with distance.
• A bar magnet is not strongest at its centre; it is strongest near the poles.