Final answer:
To use Ampère's law to find the magnetic field B(r), the path of integration must satisfy two key conditions: it must pass through the point r (Condition a) and have enough symmetry such that B(r)·dl is constant along large parts of it (Condition b). The correct choice for applying Ampère's law is option 2: a and b.
Step-by-step explanation:
The student is asking about conditions necessary to use Ampère's law to find the magnetic field B(r) at a point r. To apply Ampère's law effectively and analytically determine B(r), the chosen path for the integral must satisfy two conditions:
- The path must pass through the point r in question (Condition a).
- The path must have symmetry such that B(r)·dl is constant along significant parts of it (Condition b). This often implies that the magnetic field is tangent and constant in magnitude along the path, and mathematically, this allows the magnetic field to factor out of the integral.
While a circular path (Condition c) is a common choice due to its symmetry when dealing with a cylindrical current configuration, the path does not necessarily have to be circular for all scenarios. To analytically find B(r) using Ampère's law, the correct answer to the student's question is option 2: a and b. A circle is often used for its convenient properties in creating symmetry, but it is not the only shape that can be chosen.