Ampere's Law

cuppy

1. The problem statement, all variables and given/known data

What is the magnitude of the magnetic field at point P if a=R and b=2R (see attached image)

2. Relevant equations
Ampere's Law where integral of B ds over a closed surface = μ0I where μ0= 4πx10-7


3. The attempt at a solution

I used the formula and found after integrating (ds becomes 2*Pi*2R the circumference of the circle) that for the outer circle (radius 2R) B= μ0I/4*Pi*R

I then thought that the current through the inner circle would be in the same ratio as that of the areas of the two circles.
So inner current/outer current = Pi*(2R)^2/Pi*R^2
so inner current = 4I

i then subsituted this into my integral for the inner circle using Ampere's Law and found B for the inner circle to be equal to μ0*4I/2*Pi*R which simplifies to μ0*2I/Pi*R

the next step is what i'm having problems with as i'm not 100% certain as to what to do with these two values of B i have found. current flows in the same direction in both so i thought id have to add one B to the other but none of these answers show up in the five multiple choice options so i must have gone wrong somewhere. have i perhaps missed a crucial step along the way or was my working out in the first place off the mark? any advice would be great

cheers

Attached Thumbnails

 

Doc Al

I can't quite follow the path that you are integrating over. Rather that attempt to use Ampere's law, why not use the Biot_Savart law to calculate the magnetic field at the center of a current loop. Unless you happen to the know the formula already.