Question

The figure below shows a cross-section of two long, straight, parallel wires, where the currents are flowing perpendicular to the page. Wire 1 carries a current

I₁

directed into the page (in the

−z

direction) and passes through the x-axis at

x = +a.

Wire 2 passes through the x-axis at

x = −2a

and carries an unknown current

I₂.

The total magnetic field at the origin due to the current-carrying wires has the magnitude

2μ0I1

(2πa)

. Note that the current

I₂

can have either of two possible values.

The cross-sections of two long, straight, parallel wires are depicted on the x axis. The cross-section of the wire labeled I₁ contains a cross in the shape of an X, and is located at x = +a. The cross-section of the wire labeled I₂ is a solid color, and is located at x = −2a.

(a)

Find the value of I₂ with the smaller magnitude, stating it in terms of I₁ and giving its direction.

magnitudeI₂=

direction ---Select--- to the left to the right upward downward into the page out of the page

(b)

Find the other possible value of I₂. (Use the following as necessary: I₁.)

magnitudeI₂=

direction ---Select--- to the left to the right upward downward into the page out of the page

(c)

What If? For each of the values of

I₂,

at what location along the x-axis is the total magnetic field due to both wires equal to zero? Your answers should be in terms of a.value of I₂ from part (a)x=

value of I₂ from part (b)x=

Answer 1

olirection solution (2) Ax B= 2 UoI/ 2T a. - Best magnetic field due to I, =B1 Bi= Moli directed along ty close 2Ta. so magnetic field due to I2 = B2 and Be= Moll directed along ty ata direction - For this I, 3 2I, and directed 1 out of page 1 That is along + Z direction- magnitude Iz = 2I direction - out of Page (b) Iz of larger magnitude = 61, so B2 = Mo (GI) along -yaxi's 25 (-29) and By = Mo Il along ty axis ata. so B2-B, = 2 lol - 2na magnitude Iz = 6IL. direction → Into the page. (c) Moll - so I 1 203X = 39 from I 21TX 2 ( 34+x) so from exigin x= 49. in the right value al Iz from Pasta) X = la. value of Iz from Part (b) x= 4a.

Answer 2

A.

I_2=2I_1

out of page 

B. 

I_2=6I_1

in the page

C. 

x=4a

x=(4a)/7