Question

(a) Evaluate the closed line integral of H about the rectangular path P1(2, 3, 4) to P2(4, 3, 4) to P3(4, 3, 1) to P4(2, 3, 1) to P1, given H = 3zax − 2x3az A/m. (b) Determine the quotient of the closed line integral and the area enclosed by the path as an approximation to (∇×H)y. (c) Determine (∇×H)y at the center of the area.

Answer 1

So, what trouble are you having?

Answer 2

i need help with b and c i completed part a

Answer 3

Well, can you find the area enclosed by that loop?

Answer 4

i do not know how to do it

Answer 5

Draw the picture of those points.

Answer 6

ok

Answer 7

now what?

Answer 8

So, what's the area of that shape?

Answer 9

It should be a rectangle.

Answer 10

yes

Answer 11

Divide the value of the integral that you found by that area. That's the answer for part (b).

Answer 12

so it would be 354/6?

Answer 13

I don't know, I haven't done the integral - but that numerator seems large. Let me check.

Answer 14

ok i know the correct answer for A is 354A

Answer 15

The function is
\[ \vec H = 3z\hat x - 2x^3 \hat z \]
right?

Answer 16

yes

Answer 17

Okay, I agree. Yes, you are correct, the answer to be should be 354/6 = 59

Answer 18

Now you must find the curl of the function \(\vec H \) and evaluate it at the center of the rectangle.

Answer 19

how do i do that?

Answer 20

If you don't know what a curl is, you should consult your book or Wikipedia. it is one of the three major vector differential operators.

Answer 21

Wow Good job @Jemurray3 you couldent explained that better!

Answer 22

*Could not

Answer 23

so i should look up curl of center of the area?

Answer 24

The definition of curl is the following:

if \( \vec H = H_x \hat x + H_y \hat y + H_z \hat z \) then
\[ \nabla \times \vec H = \left( \frac{\partial}{\partial y} H_z - \frac{\partial}{\partial z} H_y\right)\hat x + \left( \frac{\partial}{\partial z} H_x - \frac{\partial}{\partial x} H_z\right)\hat y + \left( \frac{\partial}{\partial x} H_y - \frac{\partial}{\partial y} H_x\right)\hat z\]

So you need to calculate this function, and then plug in the coordinates of the center of the rectangle.


Also, thank you Holly, but I didn't really explain anything :)

Answer 25

thank you