Please solve this magnetism question?

![https://useruploads.socratic.org/GcMQFgNgR2mGIWtdZipk_imp1.jpg](useruploads.socratic.org) 1. 0 : 1 : 1
2. 0 : 1 : -1
3. 0 : 1 : 0
4. 1 : 0 : 0

1 Answer
Mar 6, 2018

Option 22

Explanation:

Apply right handed cork screw rule to determine the direction of the vec BB

So,at point AA i.e midway between the the two wire,magnetic field due to wire 11 is -(2mu_0 i)/(4 piR)2μ0i4πR direction is going into the plane of the page.

and for wire 22 it is (2mu_0 i)/(4 piR)2μ0i4πR as well but direction is coming out of the page of the plane,

So,magnetic field at point AA is (2mu_0 i)/(4 piR)-(2mu_0 i)/(4 piR)=02μ0i4πR2μ0i4πR=0

At point BB magnetic field due to wire 11 is B_1=(2mu_0 i)/(4 piR)B1=2μ0i4πR coming out of the plane of the page, and due to wire 22 it is B_2=(2mu_0 i)/(4 pi*3R)= (mu_0 i)/(6 piR)B2=2μ0i4π3R=μ0i6πR (as here distance is R+R/2=(3R)/2R+R2=3R2) direction is coming out of the plane of page.

So,net magnetic field at point BB is B_1 +B_2=BB1+B2=B (let)

Again,for point CC due to wire 22 magnetic field B_2' =-(2mu_0 i)/(4 piR) direction is going into the plane of the page,and due to wire 1 it is B_1'= -(mu_0 i)/(6 piR) (compare for wire 2 effect on point A) and the direction is going into the plane of the page.

So,net magnetic field at point C is B_1'+B_2'=B'(let)

Clearly, B=-B' (direction is opposite of each other)

So,the ratio of magnetic field at point A ,B and C is 0:1:-1