Two long parallel wires are at a distance R a | vedclass

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

Question

(B) Let the currents in both wires be $i$. The magnetic field due to a long straight wire at a distance $r$ is $B = \frac{\mu_0 i}{2 \pi r}$.Using the

Vedclass · Accepted Answer

$0 : 1 : -1$

Vedclass · Answer

(B) Let the currents in both wires be $i$. The magnetic field due to a long straight wire at a distance $r$ is $B = \frac{\mu_0 i}{2 \pi r}$.Using the right-hand rule,the magnetic field at point $A$ (midpoint between wires) due to wire $1$ is directed into the page ($-k$ direction) and due to wire $2$ is directed out of the page ($+k$ direction). Since the distances are equal $(R/2)$,the magnitudes are equal,so $B_A = 0$.At point $B$,both wires produce magnetic fields directed into the page. The distance from wire $1$ is $R/2$ and from wire $2$ is $3R/2$. Thus,$B_B = -\left( \frac{\mu_0 i}{2 \pi (R/2)} + \frac{\mu_0 i}{2 \pi (3R/2)} \right) = -\frac{\mu_0 i}{\pi R} (1 + 1/3) = -\frac{4 \mu_0 i}{3 \pi R}$.At point $C$,both wires produce magnetic fields directed out of the page. The distance from wire $2$ is $R/2$ and from wire $1$ is $3R/2$. Thus,$B_C = +\left( \frac{\mu_0 i}{2 \pi (R/2)} + \frac{\mu_0 i}{2 \pi (3R/2)} \right) = +\frac{4 \mu_0 i}{3 \pi R}$.The ratio $B_A : B_B : B_C = 0 : -\frac{4 \mu_0 i}{3 \pi R} : \frac{4 \mu_0 i}{3 \pi R} = 0 : -1 : 1$. Note: The options provided in the source are $0 : 1 : -1$. Depending on the sign convention for direction,$0 : 1 : -1$ is equivalent to $0 : -1 : 1$.

Two long parallel wires are at a distance $R$ apart. They carry steady equal currents in the same directions as shown in the figure. The ratio of magnetic fields at $A, B$ and $C$ respectively,is

Similar Questions

Two similar coils are kept mutually perpendicular such that their centres coincide. At the centre,find the ratio of the magnetic field due to one coil and the resultant magnetic field by both coils,if the same current is flowing through them.

In the figure,what is the magnetic field at the point $O$?

$A$ coil having $N$ turns carries a current $I$ as shown in the figure. The magnetic field intensity at point $P$ is

Two parallel conducting wires of equal length are placed distance $d$ apart and carry currents $I_1$ and $I_2$ respectively in opposite directions. The resultant magnetic field at the midpoint of the distance between both the wires is

Vedclass Test Series

Exam Paper Generator

Online Exam Module