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K sorry for the bad drawing using paint...but anyways...so the question is :A long wire is in a conducting sheath and viewed from the top.The wire and the conducting sheath each carry opposite currents I into and out of the page with current density as J.The outer sheath has a radius of 2R and he inner wire has a radius of R from the centre.Calculate the magnetic field at the centre of the wire.

J=I/A->I=JA

Taking the amperian loop as a circle of radius 2R

A= pir^2....I1= pi (R^2)I and I2= 4pi(R^2)I

therefore the net current wud be I2-I1 which is 3(pi)(R^2)

then using ampere's law B(2(pi)r)=(mu)I -> B(2(pi)(2R))=3(pi)(R^2)

And I get (3/4)(pi)R^2)J...but the answer is (1/2)(pi)R^2)J

Can you please tell me wht I am doing wrong?Please help me quickly I have an AP C exam tomorrow and I want to make sure I knw how to use Ampere's law porperly.Thank You

Btw if possible can you explain to me wht exactly is happening...if there is a current going in one direction...how come the sheath carries a current in the opposite direction?

J=I/A->I=JA

Taking the amperian loop as a circle of radius 2R

A= pir^2....I1= pi (R^2)I and I2= 4pi(R^2)I

therefore the net current wud be I2-I1 which is 3(pi)(R^2)

then using ampere's law B(2(pi)r)=(mu)I -> B(2(pi)(2R))=3(pi)(R^2)

And I get (3/4)(pi)R^2)J...but the answer is (1/2)(pi)R^2)J

Can you please tell me wht I am doing wrong?Please help me quickly I have an AP C exam tomorrow and I want to make sure I knw how to use Ampere's law porperly.Thank You

Btw if possible can you explain to me wht exactly is happening...if there is a current going in one direction...how come the sheath carries a current in the opposite direction?