Magnetic Field inside a current carrying wire

[darkar]

Homework Statement

A cable with given diameter D1 is given, a small hole with diameter D2 is drilled on it. The axis of them are parallel and the distance between the axis are given as r. There is a uniform steady current density flowing through it. How to calculate the magnetic field at the center of cable and center of the hole?

I have problem on how to start with the question. I am not sure which point the magnetic field is pointing and also, if i use ampere's law, i m using the closed path including outside. Thinking of Using Biot Savart law, but still i m having trouble in figuring out the direction of magnetic field.

Thanks

 

[darkar]

Hmm, i just rethink again, maybe i should first use Amperes law to find the relationship of magnetic field inside the wire, then use superposition of the de-magnetic field due to the hole and add them up together.#

Just a guess, is the magnetic field still a circle inside the wire? (assuming no hole in this case).

 

[chanvincent]

Just a guess, is the magnetic field still a circle inside the wire? (assuming no hole in this case).

Yes, the magnetic field is "always" a closed loop... regardless of "everything"...

, if i use ampere's law, i m using the closed path including outside.

Not quite right... you want to know the B field inside the hole, therefore the closed path
shall not fall outside the inner diameter... if that is the case, what can you conclude from
this?

Thinking of Using Biot Savart law,

If you want to use Biot Savart law, the B field must perpendicular to the direction of
the current flow, however, since the current is surrounding you, you could argue that
the B field could not point to any of these direction otherwise the whole picture is not
"symmetric" anymore, thus the field must be zero.

 

[squiggles0]

sorry to hijack the thread but i am doing a question very similar to darkar's and am just wondering; do you use a closed curve centred on the axis of the wire or on the centre of the hole to work out the magnetic field in the hole? My guess would be the centre of the hole, but do you consider the hole to be similar, for example, to the hole in the centre of a solenoid or do you treat it completely differently?

 

[Gokul43201]

HINT: Can you reconstruct the current flowing through the given cable by a superposition of currents flowing through simpler geometries?