Force Between Parallel Currents
For two long parallel wires separated by d in vacuum, F/L = mu_0 I_1 I_2/(2pi d) in magnitude. The sign or direction follows the current senses.
Why this shows up in the exam
Comparing force after current or distance changes · Determining attraction or repulsion · Wire-equilibrium and definition-of-ampere style problems
Learn the idea
Parallel currents attract when they flow the same way and repel when they flow in opposite directions. One wire creates a circular magnetic field at the other; that field pushes the second wire. Reversing one current reverses the force direction.
🧠 Memory hook: Same-way currents stay together; opposite-way currents push apart.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- F/L = mu₀ I₁ I₂/(2 pi d) — force per length between ideal long parallel wires
- B₁(d) = mu₀ I₁/(2 pi d) — field of wire 1 at wire 2
How to approach it
- 1Find the field of one wire at the other
- 2Use I L cross B for direction
- 3Scale with I₁ I₂/d
Common slip-ups that cost marks
- •Using d squared in the denominator
- •Forgetting that both currents multiply
- •Applying the formula to short nonparallel segments
🌟 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.
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