An infifnitely long conductor `PQR` is bent to form a right angle as shown in figure. 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 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_2`. 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)=` Magnetic field adt M due to PQ + Magnetic field at M due to QR
But magnetic field at M due to QR=0
`:.` Magnetic field at M due to PQ (or due to current l in PQ)= `H_(1)`
Now `H_(2)=` Magnetic field at M due to PQ (current l)
+ magnetic fiedl at M due to QS (curent `l//2`) , + magntetic field at M due to QR
`=H_(1)+(H_(1))/2+0=3/2H_(1), (H_(1))/(H_(2))=2/3`
Note : Magnetic field at any point lying on the current carrying straight conductor is zero.