Consider a long, straight, thin wire carrying a steady current. The value of $\oint \vec { B } \cdot d \vec { s }$ computed around a circle at some radius (orthogonal from the wire) is
A) larger as the radius is increased.
B) smaller as the radius is increased.
C) constant (not a function of the radius).
D) none of the above.

Question

Quizplus · Accepted Answer

The value of $\oint \vec { B } \cdot d \vec { s }$ around a circle at some radius from a long, straight, thin wire carrying a steady current is given by Ampère's law, which states that this integral is equal to $\mu_0 I$ (where $I$ is the current through the wire), independent of the radius of the circle. This means the magnetic field's contribution along the path is constant regardless of the radius, assuming the path encloses the current-carrying wire.

Consider a Long, Straight, Thin Wire Carrying a Steady Current ∮B⃗⋅ds⃗\oint \vec { B } \cdot d \vec { s }∮B⋅ds

Consider a Long, Straight, Thin Wire Carrying a Steady Current $\oint \vec { B } \cdot d \vec { s }$