Field Inside a Long Solenoid
For an ideal long air-core solenoid with n turns per unit length, B = mu_0 n I inside and approximately zero outside. End effects are neglected.
Why this shows up in the exam
Designing uniform laboratory fields · Finding turn density from field data · Combining solenoid fields with charged-particle motion
Learn the idea
A long tightly wound solenoid has an almost uniform interior field set by turns per length and current. Many circular turns reinforce one another inside and largely cancel outside. The result is a nearly uniform field away from the ends.
🧠 Memory hook: Long solenoid: turns per metre times current sets the inside field.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- B_inside = mu₀ n I — uniform interior field of an ideal long air-core solenoid
- n = N/L — turn density for N turns over length L
- B_end approximately B_inside/2 — on-axis field at an open end of a very long solenoid
How to approach it
- 1Check the long-solenoid assumption and position
- 2Compute n = N/L in SI units
- 3Use B = mu₀ nI and then apply any particle relation
Common slip-ups that cost marks
- •Using total turns instead of turns per length
- •Treating the outside field as exactly zero for a short real solenoid
- •Ignoring the half-field end result
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A charge of 2 microC moves perpendicular to a 3 T magnetic field at 4 x 10^5 m/s. Find the magnetic force.
More from Magnetic Effects of Current and Magnetism
Magnetic field due to currents
Learn how electric currents produce magnetic fields, including the use of Biot-Savart law, Ampere's law, and the calculation of fields for various conductor shapes such as straight wires, circular loops, and solenoids.
Magnetic moment and properties of magnets
Explore the concept of magnetic moment for current loops and bar magnets, properties of divided magnets, and effective length of magnets.
Magnetic properties of materials
Learn about diamagnetic, paramagnetic, and ferromagnetic materials, their magnetic susceptibility, temperature dependence, Curie temperature, and the role of domains.
Force and motion in magnetic fields
Understand the forces experienced by current-carrying conductors and moving charges in magnetic fields, including the Lorentz force, force between parallel conductors, and the motion of charged particles.
Magnetic dipoles and torque
Study the behavior of magnetic dipoles in magnetic fields, including torque, potential energy, and the vector addition of dipole moments.
Galvanometer conversion and measurement devices
Understand how to convert a galvanometer into an ammeter or voltmeter using shunt and series resistances, and the principles behind these measuring instruments.