Ampere loops for symmetric currents

Science · Electricity & Magnetism · ages 19-21

Name ______________________ Date ____________

The field outside an ideal long solenoid is nearly zero.
Circle one: True False
What does Ampere's law relate?
- Loop integral of B to enclosed current
- Flux of E to enclosed charge
- Induced EMF to changing flux
Which loop suits a straight wire?
- A sphere around the wire
- A circle centred on the wire
- A rectangle far from the wire
What is the field inside a toroid with N turns at core radius r?
- Mu0 N I over 2 pi r
- Mu0 n I independent of r
- Mu0 I over 2 R of the wire
A uniform thick wire has radius a. At r equals a over 2, what fraction of the current is enclosed?
Answer: ______________
Your loop encloses 9 A forward and 7 A back. What counts?
- 16 A, adding all magnitudes
- 9 A, counting only forward currents
- 2 A, the net enclosed current
A solenoid field is 2 units. Turns per length triple and current halves. Give the new field in the same units.
Answer: ______________
A student pulls B out of the integral for a short finite wire. What is wrong?
- Mu0 has the wrong value there
- B varies along every loop, so no symmetry helps
- Ampere's law only works for zero current

Answer key

For grown-ups. Fold this page away before handing over the rest.

True · The rectangle loop shows the field lives inside the windings.
Loop integral of B to enclosed current · Ampere links circulation of B to mu0 times enclosed current.
A circle centred on the wire · On the centred circle B is constant and parallel to the path.
Mu0 N I over 2 pi r · A circular loop through the core encloses N I in total.
0.25 · Enclosed current grows with r squared, and one half squared is one quarter.
2 A, the net enclosed current · Signs from the right-hand rule leave a net of 2 A.
3 · Field follows n I, so 3 times one half of 2 is 3.
B varies along every loop, so no symmetry helps · Without symmetry B cannot factor out, so the law gives no direct B.