Answered

Join the IDNLearn.com community and start getting the answers you need today. Our platform is designed to provide reliable and thorough answers to all your questions, no matter the topic.

Two long parallel wires 20 cm apart carry currents of 5.0 A and 8.0 A in the between the two wires where the magnetic field is zero?
a. yes, midway between the wires
b. yes, 12 cm from the 5-A wire
c. yes, 7.7 cm from the 5-A wire
d. no

Sagot :

Onyebuchinnajiidn

Answer:

c. yes, 7.7 cm from the 5-A wire

Explanation:

Given;

distance between the two wires, r = 20 cm = 0.2 m

first current, I₁ = 5.0 A

second current, I₂ = 8.0 A

The magnetic field due to the two wires occurs in different directions and it can be zero at this region.

Let x be the distance from 5 A wire where the magnetic field is zero.

[tex]B = \frac{\mu_o}{2\pi} [\frac{I_1}{x} -\frac{I_2}{r-x} ] = 0\\\\ \frac{\mu_o}{2\pi} [\frac{I_1}{x} -\frac{I_2}{r-x} ] = 0\\\\ \frac{\mu_o}{2\pi} [\frac{5}{x} -\frac{8}{0.2-x} ] = 0\\\\\frac{5}{x} -\frac{8}{0.2-x} = 0\\\\\frac{5}{x} = \frac{8}{0.2-x}\\\\5(0.2-x) = 8x\\\\1 -5x = 8x\\\\1 = 5x \ + \ 8x\\\\1 = 13x\\\\x = \frac{1}{13} \\\\x = 0.077 \ m\\\\x = 7.7 \ cm[/tex]

Therefore, the correct option is c. yes, 7.7 cm from the 5-A wire

Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.