A rabbit has eaten the foil shielding off of a power cable that carries a DC current of I = 0.21 A to the amplifier for your outdoor speaker system. The shielded parts of the wire do not contribute to the magnetic field outside the wire. The unshielded part of the wire is x = 0.018 meters long. Point A is exactly above the midpoint of the unshielded section, a distance x/2 above the wire. The current flows to the right as shown, which should be taken as the positive direction. The small length of wire, dl, a distance l from the midpoint of the unshielded section of the wire, contributes a differential magnetic field dB, at point A.
Randomized Variables
I = 0.21 A
x = 0.018 m
(a) Choose the expression for the magnitude of the differential magnetic field, dB, generated at point A by the current moving through the segment of wire dl, in terms of given parameters and fundamental constants.
(b) Perform the indefinite integral you found in part (a). Leave your answer in terms of x and l.
(c) Select the limits of integration that will correctly calculate the magnetic field at A due to the current in the unshielded length of wire.
(d) Evaluate the expression for the magnetic field at point A using the endpoints chosen in part (c).
(e) Determine the strength of the magnetic field, in tesla, at point A.
(f) In what direction will the magnetic field point at point A due to the current in the unshielded portion of the wire?