Question

An infinitely 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 carrying conductor a the point $M$ is $B_1$. Now, another infinitely long straight conductor $QS$, is connected at $Q$ so that the current is $\frac{1}{2}I$ is $QR$ as well as in $QS$, the current in $PQ$ remaining unchanged. The magnetic field at $M$ is now $B_2$. the ration $B_1/B_2$ is given by

• A. $1/2$
• B. $1$
• C. $2/3$
• D. $2$

Answer 1

The correct option is C $2/3$

$\overrightarrow{B_1}=\frac{{\mu }_{0}I}{4\pi R}⨀,$
$\overrightarrow{B_2}=\frac{{\mu }_{0}I}{4\pi R}+\frac{{\mu }_{0}I/2}{4\pi R}⨀$

$\Rightarrow B_2=\frac{{\mu }_{0}I}{4\pi R}\left(\frac{3}{2}\right)⨀$
$\Rightarrow \left|\frac{B_1}{B_2}\right|=\frac{2}{3}$