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An infinitely long conductor PQR is ben...

An infinitely long conductor ` PQR` is bent to form a light 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

A

`1/2`

B

`1`

C

`2/3`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
C
Case 1 : magnetic field at `M` due to ` PQ and QR` is
`H_(1) = 1/2 [ (mu_(0)I)/(2 pi R )] + 0 = ( mu_(0)I)/( 4 pi r)`
Case 2 : when wire ` QS ` is joined .
` H_(2) = ( Magnetic field at M due to PQ) + ( Magnetic field at M due to QR) + ( Magnetic field at M due to QS)`
= 1/2 [ (mu_(0)I)/( 2 pi R)] + 0 + 1/2 [ (mu_(0)//2)/(2 pi R)] = (3 mu_(0)I)/(8 pi R) :. (H_(1))/(H_(2)) = 2/3`

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