Two very long straight parallel wires,paralle | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let a point $P$ be at a distance $x'$ from the wire at $(-d, 0, 0)$. The distance from the wire at $(d, 0, 0)$ is $(2d - x')$.Using the right-hand

Vedclass · Accepted Answer

Vedclass · Answer

(C) Let a point $P$ be at a distance $x'$ from the wire at $(-d, 0, 0)$. The distance from the wire at $(d, 0, 0)$ is $(2d - x')$.Using the right-hand rule,the magnetic field $B_z$ at point $P$ due to the wire at $(-d, 0, 0)$ carrying current $I$ in $-y$ direction is $B_1 = \frac{\mu_0 I}{2 \pi x'}$ (directed into the page,i.e.,$-z$ direction).The magnetic field $B_z$ due to the wire at $(d, 0, 0)$ carrying current $4I$ in $+y$ direction is $B_2 = \frac{\mu_0 (4I)}{2 \pi (2d - x')}$ (directed into the page,i.e.,$-z$ direction).Since both fields are in the same direction,the total field is $B_z = -\frac{\mu_0}{2 \pi} \left( \frac{I}{x'} + \frac{4I}{2d - x'} ight)$.As $x' 	o 0$ or $x' 	o 2d$,$B_z 	o -\infty$. The magnitude $|B_z|$ has a minimum where $\frac{d|B_z|}{dx'} = 0$.$\frac{d}{dx'} \left( \frac{1}{x'} + \frac{4}{2d - x'} ight) = -\frac{1}{(x')^2} + \frac{4}{(2d - x')^2} = 0 \Rightarrow (2d - x')^2 = 4(x')^2 \Rightarrow 2d - x' = 2x' \Rightarrow x' = \frac{2d}{3}$.At $x' = \frac{2d}{3}$,the field magnitude is minimum. The graph shows a $U$-shaped curve with vertical asymptotes at the wire positions,which matches option $C$.

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.

Similar Questions

Two concentric loops $A$ and $B$ of same radius $R = 2 \pi \,cm = 2 \pi \times 10^{-2} \,m$ are placed at right angles to each other. If the currents flowing through $A$ and $B$ are $I_A = 3 \,A$ and $I_B = 4 \,A$ respectively, then the net magnetic field at their common centre is:

The dimensional formula of $\frac{1}{2} \mu_0 H^2$ (where $\mu_0$ is the permeability of free space and $H$ is the magnetic field intensity) is:

Choose the correct sketch of the magnetic field lines for a pair of parallel current-carrying wires,one with current flowing into the plane (represented by $\otimes$) and one with current flowing out of the plane (represented by $\odot$).

The unit of magnetic flux density (or magnetic induction) is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module