Question

Why do the two straight segments in the semicircular arc example contribute no magnetic field at the centre?

Options

• The current in the straight segments is zero

• Their magnetic fields point along the arc and cancel the curved part

• The straight segments are infinitely far from the centre

• The direction from each point to the centre is along the wire itself, making \(dl\times r=0\)

Answer 1

For each straight segment, the direction from a point on the wire to the centre is along the wire itself. Thus the cross product \(dl\times r\) is zero, so the segments contribute nothing.