Solenoid Magnetic Field Calculator

An ideal solenoid is a long helical coil with n turns per unit length carrying current I. Inside the mid-region (far from ends), the field is uniform, parallel to the axis, and given by B = μ₀nI. This is derived from superposing fields of many circular loops or by applying Ampère's law to a rectangular Amperian loop straddling the interior.

Turn density n = N/L where N is total turns and L is solenoid length in meters. Example: 500 turns/m with I = 2 A gives B = (4π×10⁻⁷)(500)(2) ≈ 1.26×10⁻³ T ≈ 1.3 mT — strong enough to pick up paper clips with an iron core.

Inserting a ferromagnetic core multiplies the field: B = μ₀μ_r nI where μ_r can exceed 1000 for soft iron at moderate fields. Electromagnets, relays, and doorbell ringer coils exploit this. Saturation limits B at high I when core domains align.

Outside an ideal infinite solenoid, B ≈ 0. Real finite solenoids show fringing at ends where field lines bulge outward. A toroid (coil bent into a donut) confines all field lines inside the core with negligible external field — used in transformers and inductors.

Solenoids are the magnetic analog of parallel-plate capacitors for uniform fields. MRI gradient coils, particle detector magnets, and lab demagnetizers all use solenoid geometry or stacks thereof.

Class 12 compares solenoid and toroid fields; JEE may ask to find n or I given target B inside a given geometry.