Question

Name -20 A 2.2 cm 1.1 cm 1 33 A Find the magnetic field at the center of the loop from both sources. Assume all currents are constant. (5pt) (a) The current in the long straight wire is reversed (and the system stabilizes so ignore any induction effects). What is the magnetic field at the center of the loop now? (5 pt) (b)

Answer 1

a)

due to the loop :

i = current in the loop = 20 A

r = radius of the loop = 2.2/2 = 1.1 cm = 0.011 m

magnetic field due to current in loop is given as

B_loop = ($\mu$/4$\pi$) (2$\pi$i/r)

B_loop = (10^-7) (2 x 3.14 x 20/0.011) = 1.14 x 10^-3 T

due to the straight wire :

i = current in the loop = 33 A

r = radius of the loop = 2.2/2 + 1.1 = 2.2 cm = 0.022 m

magnetic field due to current in straight wire is given as

B_s = ($\mu$/4$\pi$) (2i/r)

B_s = (10^-7) (2 x 33/0.022) = 0.3 x 10^-3 T

net magnetic field is given as

B = B_s + B_loop = 0.3 x 10^-3 + 1.14 x 10^-3 = 1.34 x 10^-3 T

b)

net magnetic field is given as

B = - B_s + B_loop = - 0.3 x 10^-3 + 1.14 x 10^-3 = 8.4 x 10^-4 T