3. Two long, straight, parallel wires perpendicular to the...

3. Two long, straight, parallel wires perpendicular to the xy-plane, each have a current $I$ but in opposite directions and are a distance $2a$ from each other as shown in the figure below. A point $P_1$ is located at the origin and $P_2$ is located at a distance $\frac{3}{2}a$ to the right of the origin. Answers should be in terms of $I$, $a$, and physical constants. y $\uparrow$ $O$ $I$ $a$ $P_1$ $\frac{3}{2}a$ $P_2$ $x$ $\downarrow$ $I$ 3.1) Find the magnitude and direction of the magnetic field at the origin $P_1$. (+1.5) 3.2) Find the magnitude and direction of the magnetic field at the point $P_2$. (+2)

Transcript

00:01 Hello, in the question we have given that two cross -sections of a long parallel wires are arranged on the corner of square.

00:08 So, this is the configuration given in the question and the currents, the currents are given i1 and i2 which is 2f and 4g.

00:16 So, now this b1 and b2 i have represented by using the right -hand thumb rule.

00:21 So, if we use the right -hand thumb rule for current i1, so i1 is coming out of the page.

00:27 So, if we place the fingers pointing towards us and call the finger, so we will find that this b1 is pointing in this direction.

00:36 So, b1 is the magnetic field due to this current i1.

00:39 Now, this b2, b2 now this i2, same we will do for i2, i2 is coming out of the page.

00:46 So, we will place the finger in the direction towards us, pointing towards us and we will call the fingers.

00:52 We will find that the magnetic field is along this direction, the tangential one.

00:57 So, now having done this, so we know that for the infinitely long current carrying wire, the magnetic field is given by mu naught i divided by 2 pi r.

01:10 So, b1 will be equal to mu naught i divided by 2 pi r.

01:14 So, current is i1 and b2 will be equal to mu naught i2 divided by 2 pi r.

01:20 R is the distance, that is the edge length of the square.

01:25 So, let us compute b1.

01:27 So, b1 will be equal to mu naught is 4 pi into 10 raised to minus 7 into i1 is 2f divided by 2 pi into r.

01:41 R is how much? 20 centimeters, so which is 0 .2 meters.

01:46 So, if we calculate, so this 2, 2 goes away, this pi goes away, this 2, so this becomes 10.

01:51 So, it gives us b1 as 20f into 10 raised to minus 7 tesla.

01:59 So, similarly, we can find out b2.

02:01 So, b2, what it will be? mu naught 4 pi into 10 raised to minus 7 into b2 is 4g divided by 2 pi r is 0 .2.

02:18 So, if this pi goes away, 2 ones are 2, 2 twos are 4, then this becomes 10.

02:23 So, this becomes 40 into 10 raised to minus 7 and g, g will be there over here multiplied with 40...

Question

Please give Ace some feedback