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An infifnitely long conductor PQR is ben...

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 `

A

`1//2`

B

`1`

C

`2//3`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
C
(c) Case1: Magnetic field at M due to PQ and QR is

`H_1=1/2[(mu_0I)/(2piR)]+0=(mu_0I)/(4piR)`
Case2: When wire Q 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_0I)/(2piR)]+0+1/2[(mu_0I//2)/(2piR)]=[(3mu_0I)/(8piR)]`
`:. (H_1)/(H_2)=2/3`
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