Magnetic field of coils
Two thin coils of radius R = 4 cm are x = 24 cm apart andconcentric with a common axis. Both coils contain 10 turns of wirewith a conventional current of I = 3 amperes that runscounter-clockwise as viewed from the right side (see thefigure).
(a) What is the magnitude and direction of the magnetic field onthe axis, halfway between the two loops, without making theapproximation z >> r? (For comparison, remember that thehorizontal component of magnetic field in the United States isabout 2 multiplied by 10-5 tesla).
|B| =
(b) In this situation, the observation location is not very farfrom either coil. Calculate the magnitude of the magnetic field atthe same location, using the 1/z3 approximation.
|Bapprox| = 3 T
The percent error of an approximate result can be found by100*abs(1-(approx)/(exact)). What percentage error results if youcalculate the magnetic field using the approximate formula for acurrent loop instead of the exact formula?
4% error
(c) What is the magnitude and direction of the magnetic fieldmidway between the two coils if the current in the right loop isreversed to run clockwise?
Magnetic field of coils
Two thin coils of radius R = 4 cm are x = 24 cm apart andconcentric with a common axis. Both coils contain 10 turns of wirewith a conventional current of I = 3 amperes that runscounter-clockwise as viewed from the right side (see thefigure).
(a) What is the magnitude and direction of the magnetic field onthe axis, halfway between the two loops, without making theapproximation z >> r? (For comparison, remember that thehorizontal component of magnetic field in the United States isabout 2 multiplied by 10-5 tesla).
|B| =
(b) In this situation, the observation location is not very farfrom either coil. Calculate the magnitude of the magnetic field atthe same location, using the 1/z3 approximation.
|Bapprox| = 3 T
The percent error of an approximate result can be found by100*abs(1-(approx)/(exact)). What percentage error results if youcalculate the magnetic field using the approximate formula for acurrent loop instead of the exact formula?
4% error
(c) What is the magnitude and direction of the magnetic fieldmidway between the two coils if the current in the right loop isreversed to run clockwise?
