Question

II. Symmetry as an aid in calculating B You want to determine the magnet field at a point on the y axis due to a ring of current centered on the y axis as shown. The ring is a circle and circles have symmetry. There are numerous ways objects can be symmetric. One of them is rotational symmetry, meaning that everything looks the same no matter how much you rotate the object about a particular axis. About which axis(es) is the ring symmetric? R Looking at the angle between dĩ and ř, does that angle change? What does that mean about the magnitude of dő? Remembering that the magnetic field is a vector product, which component of dB changes as dl moves around the ring? Which component stays constant? Explain your reasoning. Determine the magnetic field at a point on the y axis without integrating.

Answer 1

y axis NO. between doesn't is same due to all Ring is symmetric about Angle change. Magnitude of df elements of ring. Component of dB perpendicular to → component of dB parallel to plane of ring changes while the component of dB along y-axis remains same. By symmetry dB To Idl R MTÍ 02 + y²g 3/2 .. total B is just due to all de elements B Mo 25R²1 477 (y?72362