Answered

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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

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