Magnetics 2 Question 4
4. Two very long, straight and insulated wires are kept at $90^{\circ}$ angle from each other in $x y$-plane as shown in the figure
These wires carry currents of equal magnitude $I$, whose directions are shown in the figure. The net magnetic field at point $P$ will be
(2019 Main, 8 April II)
(a) zero
(b) $\frac{+\mu _0 I}{\pi d}(\hat{\mathbf{z}})$
(c) $-\frac{\mu _0 I}{2 \pi d}(\hat{\mathbf{x}}+\hat{\mathbf{y}})$
(d) $\frac{\mu _0 I}{2 \pi d}(\hat{\mathbf{x}}+\hat{\mathbf{y}})$
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Answer:
Correct Answer: 4. (a)
Solution:
- Magnetic field due to an infinitely long straight wire at point $P$ is given as
Thus, in the given situation, magnetic field due to wire 1 at point $P$ is
Similarly, magnetic field due to wire 2 at point $P$ is
$$ \mathbf{B} _2=\frac{\mu _0}{2 \pi} \frac{I}{d} $$
Resultant field at point $P$ is
$$ \mathbf{B} _{net}=\mathbf{B} _1+\mathbf{B} _2 $$
Since, $\left|\mathbf{B} _1\right|=\left|\mathbf{B} _2\right|$, but they are opposite in direction.
Thus, $\mathbf{B} _{\text {net }}=0$
$\therefore$ Net magnetic field at point $P$ will be zero.
