Direction of force in current carrying conductor?

Question

Question:

A staright conductor of circular cross section carries a current then, which of the following statement is true:

(a)No force act on conductor at any point

(b) An axial force act on conductor to decrease it's length

(c)A radial force acts towards axis tending to reduce it's cross section

(d)A radial force acts away from the axis tending to increase it's cross section

my thoughts( i'm doing some conceptual mistake):

i thought if a current I is going in upwards direction in a straight wire as

shown below :

then, any differential length of wire will experiance no force

but answer is not option (a) (so, wire will experiance force either in radial or axial direction )

thus, i'm having problem in understanding this concept

i'm asking why wire will experiance force from it's own magnetic field. can

anyone explain it to me ?

regards

Answer 1

We use a large circular cross-section of the wire, carrying uniform current density and apply Ampère's Law. Consider a concentric circular Ampèrian loop within the wire itself. This loop encloses some current (although not all). Thus, we can see that there will be a magnetic field inside the wire as well, pointing in the same direction as the magnetic field outside the wire. Now, consider the remaining current that is still inside this wire, but outside the Ampèrian loop. Applying the Lorentz force law $\vec F = I \vec L \times \vec B$, we see that there is a radial inward force.