Fields of Multiple Parallel Wires
Each ideal long wire contributes B_i = mu_0 I_i/(2pi r_i). The total field is the vector sum; in a common plane the contributions can be treated as signed perpendicular components.
Why this shows up in the exam
Midpoint fields between two wires · Neutral-point location · Comparing same-direction and opposite-direction currents
Learn the idea
For several parallel wires, compute each circular field with a sign and add the contributions at the point. At a point between wires, same-direction currents can make opposing fields while opposite-direction currents can make reinforcing fields. The geometry decides the signs.
🧠 Memory hook: Right-hand-rule every wire, then add signed fields.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- B_i = mu₀ I_i/(2 pi r_i) — field magnitude from long wire i at distance r_i
- B_net = signed_sum B_i — one-dimensional signed sum when all contributions are perpendicular to the same plane
- B_net = 0 — neutral-point condition after directions are assigned
How to approach it
- 1Mark the observation point and each distance
- 2Use the right-hand rule for every wire
- 3Add signed fields and check symmetry
Common slip-ups that cost marks
- •Assuming same-direction currents always give reinforcing fields
- •Using the wire separation for both r_i values
- •Adding magnitudes before assigning directions
🌟 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.