Magnetic field at a point due to two wires and a solenoid.

[TimeToShine]

Homework Statement

The point p is located at (3,1,2). An infinitely long straight wire passes through the points (0,0,0)
and (0;1;0) and carries a current of a A in the positive y direction. A finite length of wire carries
a current of b A from (2,0,0) to (2,0,0). An semi-infinite solenoid of n turns per metre starts at p, extends in the positive z direction towards infinity and carries a current c A flowing clockwise when viewed axially from p.


I have to find the magnetic field at P due to the three sources.

Homework Equations

Biot savart law, amperes law.

The Attempt at a Solution

Well, I've used the formula for the magnetic field B at a point due to an infinitely long current carrying conductor:

B = u0.I/(2.pi.R)

For the solenoid, would I be right in assuming that once I use the formula

B = u0.N.I

to get the magnetic field in the solenoid I can then treat it as a wire of infinite length with current C, similar to the first wire?

Since the solenoid starts at P is the magnetic field at P just equal to the magnetic field obtained from the above formula?


I'm not sure how to approach the finite length wire. I tried to find the shortest distance between it and P and then use the same formula as the infinite length wire but it gave a strange answer.

Once I get the three answers I just use superposition and add the results I presume.

Also, on another note, it says on the paper as a "hint" that no finite length wire can exist in isolation. Can anyone tell me why this is?

thanks in advance.

 

[anathema]

Hello, great question! To answer your first question, yes, you can treat the solenoid as an infinite wire with current C, similar to the first wire. The magnetic field at point P due to the solenoid can be calculated using the formula B = u0.N.I, where N is the number of turns per meter and I is the current. Since the solenoid starts at point P, the magnetic field at P will be equal to the magnetic field obtained from this formula.

For the finite length wire, you can use the Biot-Savart law to calculate the magnetic field at P. The formula is B = u0.I/(4.pi.r) where r is the distance between the point P and the current carrying wire. To find the shortest distance between the wire and P, you can use the distance formula and take the derivative with respect to the variable that represents the distance. This will give you the shortest distance between the finite length wire and point P.

The hint about no finite length wire existing in isolation is referring to the fact that a finite length wire always has a beginning and an end, and it is always connected to something else. In this case, the finite length wire is connected to the infinite wire and the solenoid, so it cannot exist on its own.

Once you have calculated the magnetic field at point P due to each source, you can use the principle of superposition to add the results and get the final magnetic field at P.

I hope this helps! Let me know if you have any further questions.