Power transported down the cable(question about electric field)

[leonne]

Homework Statement

calc the power transported down the cable

Homework Equations

S=1/$$\mu$$(E X B)

The Attempt at a Solution

I just need help in the math part.

First i found the E field and got E=$$\lambda$$/2($$\pi$$S $$\epsilon$$)) S^
B=($$\mu$$ I/2$$\pi$$s) $$\phi$$^
(note the pi and other greek letters are not exponents, not sure why it looks like it)

My question for this is where did they get the vectors from the S^ and the $$\phi$$^
I am always bad figuring what it is. Its a wire so the guess field would be a cylinder. Does it have something to do with volume? I see in my notes for volume Q= pd$$\tau$$ and next to it i have (s ds d$$\phi$$ dz) is the E field always S^?
Also one more question about that for e field i have Q=$$\lambda$$ dl where dl=L
but for the B field, in my notes its dl=2$$\pi$$S Not sure why that is.

Than for S=1/$$\mu$$(E X B)
I just make a matrix for the E and B where S^ is like X and $$\phi$$^ and Y right? The answer they get is a Z^ so i am guess that's what you do.
Than i just plug for P=integral S da Also they go about converting it into p=VI they do V=E dl than get the final answer as p=VI but if i leave it the original way it would still be right?

edit
after doing the matrix, i got the answer as $$\lambda$$$$\mu$$I/(4$$\pi$$^2$$\epsilon$$S²

and in the book, they have the same thing but no$$\mu$$ No idea how mu got canceled out
thanks

 

[mark726]

for the help
Thank you for your post. In order to calculate the power transported down the cable, you will need to use the following equation:

P = VI

Where P is the power in watts, V is the voltage in volts, and I is the current in amperes. You will also need to calculate the electric and magnetic fields using the equations you have provided. The vectors S^ and \phi^ are used to represent the direction of the electric and magnetic fields, respectively. The S^ vector points in the direction of the wire, while the \phi^ vector is perpendicular to the S^ vector and points in the direction of the magnetic field. This is because the electric and magnetic fields are perpendicular to each other in the case of a wire.

To calculate the power, you will need to integrate the P = VI equation over the surface area of the wire. This will give you the total power transported down the cable. When converting the integral to polar coordinates, you will need to use dl = Rd\theta instead of dl = L as you have mentioned. This is because the wire is in the shape of a cylinder, and you will need to integrate over the circumference of the cylinder.

As for your question about the units, the \mu term is not needed in the final equation because it is already included in the units of the electric and magnetic fields. The units for P are watts, which are equal to volts times amperes. The units for the electric field are volts per meter, while the units for the magnetic field are amperes per meter. When you multiply these units together, the units of meters cancel out, leaving you with watts.

I hope this helps you with your calculations. If you have any further questions, please feel free to post them in the forum. Good luck with your work!