Question

An infinitely long conductor PQR is bent to form 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 $\frac { 1 } { 2 }$ in QR as well as in QS, the current in PQ remaining unchanged. The magnetic field at M is now $\mathrm { H } _ { 2 }$. The ratio $H _ { 1 } / H _ { 2 }$ is given by

• A. $\frac { 1 } { 2 }$
• B. 1
• C. $\frac { 2 } { 3 }$
• D. 2

Answer 1

Answer: (C)

$\frac { 2 } { 3 }$

Answer 2

Magnetic field at any point lying on the current carrying conductor is zero.

Here H₁ = magnetic field at M due to current in PQ

H₂ = magnetic field at M due to R + due to QS + due to PQ

= $0 + \frac { H _ { 1 } } { 2 } + H _ { 1 } = \frac { 3 } { 2 } H _ { 1 }$

∴ $\frac { H _ { 1 } } { H _ { 2 } } = \frac { 2 } { 3 }$