Magnetics 2 Question 22
22. A pair of stationary and infinitely long bent wires are placed in the $x y$ plane as shown in figure. The wires carry current of $i=10 A$ each as shown. The segments $L$ and $M$ are along the $x$-axis. The segments $P$ and $Q$ are parallel to the $y$-axis such that $O S=O R=0.02 m$. Find the magnitude and direction of the magnetic induction at the origin $O$.
$(1989,6 M)$
Show Answer
Answer:
Correct Answer: 22. $10^{-4} T$, perpendicular to paper outwards
Solution:
- Magnetic field at $O$ due to $L$ and $M$ is zero. Due to $P$ magnetic field at $O$ is
$$ B _1=\frac{1}{2} \frac{\mu _0}{2 \pi} \frac{i}{O R}=\frac{\left(10^{-7}\right)(10)}{0.02}=5.0 \times 10^{-5} T $$
(perpendicular to paper outwards)
Similarly, field at $O$ due to $Q$ would be,
$$ \begin{aligned} B _2 & =\frac{1}{2} \frac{\mu _0}{2 \pi} \frac{i}{O S} \\ & =\frac{\left(10^{-7}\right)(10)}{0.02}=5.0 \times 10^{-5} T \end{aligned} $$
(perpendicular to paper outwards)
Since, both the fields are in same direction, net field will be sum of these two.
$$ \therefore \quad B _{\text {net }}=B _1+B _2=10^{-4} T $$
Direction of field is perpendicular to the paper outwards.
