Solenoid & Toroid Magnetic Field

MAGNETIC FIELDS OF SOLENOIDS AND TOROIDS

A solenoid is a long coil of wire wrapped in a helical shape. When an electric current passes through it, it produces a nearly uniform magnetic field inside the coil, similar to a bar magnet. A toroid is essentially a solenoid bent into a circle (a doughnut shape). Both are fundamental components in electromagnets, MRI machines, and particle accelerators.

AMPERE'S LAW IN ACTION

The magnetic field strength inside a solenoid depends on the current and the number of turns per unit length . According to **Ampere's Law**, the field is given by . Inside a toroid, the field is strongest near the inner radius and decreases toward the outer radius, following . There is zero magnetic field outside an ideal solenoid or toroid.

HOW TO USE THIS VISUALIZATION

1. **Select Geometry**: Toggle between a straight Solenoid and a circular Toroid. 2. **Adjust the Windings**: Change the number of turns () and the length or radius. Observe how the field lines cluster more tightly as turn density increases. 3. **Change the Current**: Adjust and watch the magnitude of the -field vectors scale in real-time. **Try This**: Set the solenoid length to 10 cm and current to 2A. Increase the number of turns. Does the field strength inside the solenoid increase linearly with ? Move the probe outside the coil—how does the field strength compare to the value inside?

CORE FORMULAS

AP EXAM CONNECTION

KEY TAKEAWAYS

• Uniform field inside solenoids.
• Field depends on turn density ().
• Toroid field follows .
• Zero field outside ideal coils.
• Used in MRI and particle traps.

PRACTICE QUESTIONS