A long thin wire carrying a current I1 = 10 A (out of page)...

Name: A long thin wire carrying a current I1 = 10 A (out of page) is located at (0, 0) and another wire carrying a current I2 = 8A (into the page) is located at (x=9cm, y=0). Find the magnitude and direction the magnetic field due to these two currents at (x=0, y=12 cm). Your solution must include a neat diagram.
Uploaded: 2023-08-14T02:10:33-08:00
Duration: 5 min 38 s
Channel: Justin Swantek
Description: A long thin wire carrying a current I1 = 10 A (out of page) is located at (0, 0) and another wire carrying a current I2 = 8A (into the page) is located at (x=9cm, y=0). Find the magnitude and direction the magnetic field due to these two currents at (x=0, y=12 cm). Your solution must include a neat diagram.

A long thin wire carrying a current I1 = 10 A (out of page) is located at (0, 0) and another wire carrying a current I2 = 8A (into the page) is located at (x=9cm, y=0). Find the magnitude and direction the magnetic field due to these two currents at (x=0, y=12 cm). Your solution must include a neat diagram.

Transcript

00:01 All right, hello.

00:01 In this question, we're given this setup, where we have a wire coming out of the page with a current of 10 amps at the origin.

00:07 And then at the point 9, 0, 9 centimeter, 0, we have another wire going into the page with some current i2 equal to 8.

00:16 And we're asked to find the net magnetic field at point p if point p is 0, 12.

00:21 So we're up on the y -axis 12 centimeters.

00:25 So in order to do this, let's go ahead and first figure out our direction here.

00:31 Let's go ahead and draw our figure.

00:33 So if i take my right hand and point my thumb out of the page, that's going to be for wire 1 here.

00:39 And i curl my fingers.

00:40 Straight above it, i'm going to have some b field pointing to the left.

00:44 So i'm going to have some b1 there.

00:46 If i take my right hand, point my thumb into the page and curl my fingers, i'm going to have at point p some b2 pointing in that direction.

00:56 Well, what is that direction? if i go ahead and draw a right triangle here between the origin, i'm going to be able to figure out what this is, what that angle theta is.

01:05 And if i go ahead and continue that line across here, this angle here will also be theta.

01:12 And i know that if i draw a horizontal line here, this angle here is also going to be theta.

01:19 And this angle right here is going to be 90 degrees.

01:23 So this is going to be, this angle here is going to be 90 minus theta if that is theta there.

01:30 So with that in mind, we can account for directionality.

01:36 So i know that my net magnetic field is going to be as a vector, just the vector sum of my two magnetic fields.

01:44 Well, i'm going to break that down into x and y components.

01:48 So in my x direction, i'm going to have, if i have my conventional axes, this, i'm going to have b2, but just the x component of b2, and then subtract all of b1, because b1's fully in the x direction.

02:03 And in the y direction, i'm going to just have b2, but just the y component.

02:07 And so i'm going to redefine this 90 minus theta as an angle, i'll call it alpha.

02:13 And so bx is going to be b2 times the cosine of alpha.

02:20 I just want the x component there, minus b1.

02:22 And by is going to be b2 times the sine of my angle.

02:28 Well, what are b1 and b2 going to be? i know that b of a wire is mu naught times i of that wire over two pi r, where r is the distance...