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1. Homework Statement

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

2. Homework 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

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

2. Homework 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