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(A) Let the positively charged beam be at $x = 0$ and the negatively charged beam be at $x = d$. Since the positive charges move in one direction and

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(A) Let the positively charged beam be at $x = 0$ and the negatively charged beam be at $x = d$. Since the positive charges move in one direction and the negative charges move in the opposite direction,the currents $I_1$ and $I_2$ produced by these beams are in the same direction. Let the distance from the first beam be $x$. The magnetic field due to the first beam is $B_1 = \frac{\mu_0 I}{2\pi x}$ (directed into the page). The magnetic field due to the second beam at distance $(d - x)$ is $B_2 = \frac{\mu_0 I}{2\pi (d - x)}$ (directed out of the page). The net magnetic field is $B = B_1 - B_2 = \frac{\mu_0 I}{2\pi} \left( \frac{1}{x} - \frac{1}{d - x} ight)$. At the midpoint $x = d/2$,$B = \frac{\mu_0 I}{2\pi} \left( \frac{1}{d/2} - \frac{1}{d/2} ight) = 0$. As $x 	o 0$,$B 	o \infty$,and as $x 	o d$,$B 	o -\infty$. This behavior is correctly represented by the graph in option $A$.

Column $I$	Column $II$
$(A)$ Two parallel wires with current in the same direction,$P$ is the midpoint.	$(p)$ The magnetic fields $(B)$ at $P$ due to the currents in the wires are in the same direction.
$(B)$ Two coaxial circular loops with current in the same direction,$P$ is the midpoint on the axis.	$(q)$ The magnetic fields $(B)$ at $P$ due to the currents in the wires are in opposite directions.
$(C)$ Two coplanar circular loops with current in opposite directions,$P$ is the midpoint.	$(r)$ There is no magnetic field at $P$.
$(D)$ Two concentric coplanar circular loops with current in the same direction,$P$ is the common center.	$(s)$ The wires repel each other.

List-$I$	List-$II$
$a$. Fleming's left-hand rule	$e$. Direction of induced current
$b$. Fleming's right-hand rule	$f$. South pole
$c$. Clockwise current	$g$. North pole
$d$. Anticlockwise current	$h$. Direction of force

Similar Questions

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Match the following:
List-$I$ List-$II$
$a$. Fleming's left-hand rule $e$. Direction of induced current
$b$. Fleming's right-hand rule $f$. South pole
$c$. Clockwise current $g$. North pole
$d$. Anticlockwise current $h$. Direction of force

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