Magnetics 2 Question 15
15. An infinitely long conductor $P Q R$ is bent to form a right angle as shown in figure. A current $I$ flows through $P Q R$. The magnetic field due to this current at the point $M$ is $H _1$. Now, another infinitely long straight conductor $Q S$ is connected at $Q$, so that current is $I / 2$ in $Q R$ as well as in $Q S$, the current in $P Q$ remaining unchanged. The magnetic field at $M$ is now $H _2$. The ratio $H _1 / H _2$ is given by
$(2000,2 M)$
(a) $1 / 2$
(b) 1
(c) $2 / 3$
(d) 2
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Answer:
Correct Answer: 15. (a, d)
Solution:
- $H _1=$ Magnetic field at $M$ due to $P Q+$ Magnetic field at $M$ due to $Q R$. But magnetic field at $M$ due to $Q R=0$
$\therefore$ Magnetic field at $M$ due to $P Q$ (or due to current $I$ in $P Q$ )
Now $H _2=$ Magnetic field at $M$ due to $P Q$ (current $I$ )
- magnetic field at $M$ due to $Q S$ (current $I / 2$ )
- magnetic field at $M$ due to $Q R$
$=H _1+\frac{H _1}{2}+0=\frac{3}{2} H _1$
$\frac{H _1}{H _2}=\frac{2}{3}$
NOTE Magnetic field at any point lying on the current carrying straight conductor is zero.
