Question

A long thin wire is bent in the shape shown below. Assume it extends to infinity in the negative and positive x directions as shown. A current i flows in the wire as shown. The radius of the half circular part is r. The point marked P is the origin.

What is the magnitude of the magnetic field at P created by the horizontal stretch of wire?
(a) μ₀i/2π
(b) μ₀i/πr
(c) μ₀i/4πr
(d) μ₀i/2πr

What is the magnitude of the magnetic field at P created by the half circular part?
(a) μ₀i/2r
(b) μ₀i/r
(c) μ₀i/2πr
(d) μ₀i/πr

What is the direction of the net magnetic field at point P?
(a) Out of the page
(b) Into the page
(c) To the left
(d) To the right

Answer 1

The magnetic field at point P from the horizontal wire segment is zero, while the magnetic field from the half circular part is µi/2r, with the direction being out of the page.

Step-by-step explanation:

The magnitude of the magnetic field at point P created by the horizontal stretch of wire is zero as the field at the center of a symmetric arrangement cancels itself out in the idealized case of an infinitely long wire. For the half circular part, we can use Ampere's Law or Biot-Savart Law to derive the magnetic field created by a current-carrying arc. The formula for the magnetic field at the center of a circular loop of radius r carrying current i is µ₀i/2r.

The direction of the magnetic field at point P created by the horizontal wire is none as it is cancelled out. However, the magnetic field direction at P due to the half circular part is out of the page, determined by the right-hand rule where the thumb points in the direction of the current and the fingers curl in the direction of the magnetic field.