What is the magnitude of the magnetic field of the wire

[oddiseas]

Homework Statement

a long straight 6mm diameter conducting wire is carrying a current of 4A.

1)What is the magnitude of the magnetic field at a point 1mm inside the surface of the wire.

2)what is the magnitude of the magnetic field at a point 2cm from the centre of the wire

Homework Equations

using amperes law:
for part 1 i got 44*10^-9

and for part 2: 50*10^-9

I wnt to make sure i have done it right though, because it is a past exam question that i don't have solutions for. So if anyone is good at these questions, it would be helpful to check my answers in case i have stuffed up.

The Attempt at a Solution

 

[kuruman]

The answers to both parts are incorrect.

 

[ApexOfDE]

how do you calculate current inside the wire? And do you notice units of all parameters when you calculate?

 

[oddiseas]

what i tried was:

diameter =6mm. At a point 1mm inside the conducting wire, diameter is 4mm, therefore r=2mm

using amperes law:

∫B⋅ds=μ₀I{Through}

ds=2πr
I{Through}=I∗((πr²)/(πR²)) where R=6mm and r =2mm
B*2πr=I∗((πr²)/(πR²))

B=μ₀Ir/2πR²
B=μ₀(4)(0.002)/2π(0.006)²

 

[ApexOfDE]

You wrote diameter = 6mm but then when you put it into eq, you wrote R=6mm.