Question

In Ampere's law, the differential ds is:

a) an infinitesimal piece of the wire that carries current i
b) in the direction of B
c) perpendicular to B
d) a vector whose magnitude is the length of the wire that carries current i
e) none of the above

Answer 1

In Ampère's law, the differential ds represents a vector that is tangent to the path element of the loop enclosing the current, not a piece of the wire, the direction of the magnetic field, or its perpendicular.

Step-by-step explanation:

In Ampère's law, the differential ds is a mathematical representation of an infinitesimally small portion of a curve or loop around which a magnetic field may be present due to an electric current. The differential ds is not a piece of the wire itself but rather a segment along the path of the imaginary loop used in the integral of Ampère's law. The direction of ds is chosen to be tangent to the path at that point and follows the right-hand rule. Hence, in Ampère's law, ds is a vector known as the path element, and the correct answer to the question is: (d) a vector whose magnitude is the length of the differential path element in the loop around the current carrying wire.