An infinetely long conductor `PQR` is bent to from a right angle as shown. A current `I` flows through `PQR`. The magnetic field due to this current at the point `M` is `H_(1)`.Now, another infinitely long straight conductor `QS` is connected at `Q` so that the current is `I//2` in `QR` as well as in `QS`, the current in `PQ` remaining unchanged. The magnetic field at `M` is now `H_(z)`, the ratio `H_(1)//H_(2)` is given by

Options

A. `1/2`
B. `1`
C. `2/3`
D. `2`

Answer

C

Explanation

`H_(1)=(mu_(0)I)/(4pid)`

At `M:`
Due to `PQ, B_(1)=(mu_(0)I)/(4pid)`
Due to `QS, B_(2)=(mu_(0)I//2)/(4pid)`
`H_(2)=B_(1)+B_(2)=3/2 (mu_(0)I)/(4pid)`
`(H_(1))/(H_(2))=2/3`