Adding up magnetism piece by piece

Science · Electricity & Magnetism · ages 19-20

Name ______________________ Date ____________

How is the direction of each contribution found?
- Cross the piece with the radial direction
- Point along the wire everywhere
- Point straight at the wire
How does one current piece's field change with distance?
- It grows with distance
- It falls as one over distance
- It falls as one over distance squared
The field of a straight wire forms circles around the wire.
Circle one: True False
What is the field at the centre of a loop of radius R carrying I?
- Mu0 I over 2 R along the axis
- Mu0 I over 2 pi R around the wire
- Zero, since the pieces cancel
At twice the distance from a straight wire, the field is what fraction of before?
Answer: ______________
Two parallel wires carry currents in opposite directions. What happens?
- They attract each other
- They push apart
- They feel no force
Two wires double both currents and double their separation. The force per length changes by what factor?
Answer: ______________
What is the field at the centre of a half loop of radius R?
- Mu0 I over R
- Mu0 I over 2 R
- Mu0 I over 4 R

Answer key

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

Cross the piece with the radial direction · The cross product of piece and radial direction sets each dB.
It falls as one over distance squared · Each Biot-Savart piece shrinks with the square of the distance.
True · Integration of the pieces gives field lines circling the wire.
Mu0 I over 2 R along the axis · Setting distance zero along the axis in the loop integral gives mu0 I over 2 R.
0.5 · The wire field falls as one over r, so doubling r halves B.
They push apart · Opposite currents sit in fields that push them apart.
2 · Force scales as I1 I2 over r, so 2 times 2 over 2 is 2.
Mu0 I over 4 R · A half loop is the theta equals pi case, giving half the full-loop field.