In the figure, two long straight wires at separation d =...

Name: In the figure, two long straight wires at separation d = 15.8 cm carry currents of i1 = 2.64 mA and i2 = 9.00i1 out of the page. (a) At what coordinate on the x axis in centimeters is the net magnetic field due to the currents equal to zero? (b) If the two currents are doubled, is the zero-field point shifted toward wire 1, shifted toward wire 2, or unchanged?
Uploaded: 2022-04-11T02:32:06-08:00
Duration: 3 min 55 s
Channel: Darshan Maheshwari
Description: In the figure, two long straight wires at separation d = 15.8 cm carry currents of i1 = 2.64 mA and i2 = 9.00i1 out of the page. (a) At what coordinate on the x axis in centimeters is the net magnetic field due to the currents equal to zero? (b) If the two currents are doubled, is the zero-field point shifted toward wire 1, shifted toward wire 2, or unchanged?

In the figure, two long straight wires at separation d = 15.8 cm carry currents of i1 = 2.64 mA and i2 = 9.00i1 out of the page. (a) At what coordinate on the x axis in centimeters is the net magnetic field due to the currents equal to zero? (b) If the two currents are doubled, is the zero-field point shifted toward wire 1, shifted toward wire 2, or unchanged?

Transcript

00:01 In the figure two long straight wires at separation d is equal to 15 .8 centimeter carry currents of i1 as 2 .64 millie -amper and i -2 as 9.

00:15 Is that 9 times i -1? this looks like it's 9 -i -1.

00:19 I -2 is 9 times i -1.

00:21 It's out of the page.

00:22 At what coordinate on the x -axis in centimeters, the net magnetic field, 0? and the two currents are doubled.

00:29 Is the 0 point shifted towards 1 or 2 are unchanged? so they are towards the same direction.

00:37 So definitely in the mid, in let's say, x units from the i1, x units from the i1, let's say, the net electric, sorry, the net magnetic field.

00:53 So using the right -hand curl rule, we placed our right hand such that the thumb points towards the current, and the curly fingers will give the direction of magnetic field at that point.

01:03 So the curly finger are actually pointing upward in this case and over here as over on the left they are pointing downwards.

01:12 So for them to be zero, they should be equal right.

01:15 So individual magnetic fields should be equal because they are in opposite direction.

01:21 So mu not i1 by 2 pi x should be equal to mu not i2 by 2 pi d minus x because their distance between them is d right.

01:32 So definitely that this distance, remaining distance, is going to be d minus x.

01:37 So this mu not over 2 pi and mu not over 2 pi is cancelled.

01:40 We are left with i1 is 2 .64 millie -amper over x, and that is equal to i2, which is nine times of i -1.

01:49 So let's in fact not write the value of i -1...

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