Two parallel wires in the plane of the paper | vedclass

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

Question

(A) The magnetic field $B$ at a distance $x$ from a wire carrying current $I$ is given by $B = \frac{\mu_0 I}{2 \pi x}$.Case $1$: Currents in the same

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(A) The magnetic field $B$ at a distance $x$ from a wire carrying current $I$ is given by $B = \frac{\mu_0 I}{2 \pi x}$.Case $1$: Currents in the same direction.The magnetic fields due to the two wires at distance $X_1$ and $(X_0 - X_1)$ are in opposite directions. The net magnetic field $B_1$ is:$B_1 = \left| \frac{\mu_0 I}{2 \pi X_1} - \frac{\mu_0 I}{2 \pi (X_0 - X_1)} \right| = \frac{\mu_0 I}{2 \pi} \left| \frac{X_0 - 2X_1}{X_1(X_0 - X_1)} \right|$.Given $\frac{X_0}{X_1} = 3$, so $X_0 = 3X_1$. Substituting this:$B_1 = \frac{\mu_0 I}{2 \pi} \left| \frac{3X_1 - 2X_1}{X_1(3X_1 - X_1)} \right| = \frac{\mu_0 I}{2 \pi} \left( \frac{X_1}{2X_1^2} \right) = \frac{\mu_0 I}{4 \pi X_1}$.Case $2$: Currents in opposite directions.The magnetic fields due to the two wires are in the same direction. The net magnetic field $B_2$ is:$B_2 = \frac{\mu_0 I}{2 \pi X_1} + \frac{\mu_0 I}{2 \pi (X_0 - X_1)} = \frac{\mu_0 I}{2 \pi} \left( \frac{X_0 - X_1 + X_1}{X_1(X_0 - X_1)} \right) = \frac{\mu_0 I}{2 \pi} \left( \frac{X_0}{X_1(X_0 - X_1)} \right)$.Substituting $X_0 = 3X_1$:$B_2 = \frac{\mu_0 I}{2 \pi} \left( \frac{3X_1}{X_1(2X_1)} \right) = \frac{3 \mu_0 I}{4 \pi X_1}$.The radius of curvature is $R = \frac{mu}{qB}$, so $R \propto \frac{1}{B}$.Therefore, $\frac{R_1}{R_2} = \frac{B_2}{B_1} = \frac{3 \mu_0 I / 4 \pi X_1}{\mu_0 I / 4 \pi X_1} = 3$.

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 current-carrying conductor $(AOCDEFG)$ as shown,the magnetic induction at the point $O$ is ($R_1$ and $R_2$ are radii of arcs $CD$ and $EF$ respectively,$I$ = current in the loop,$\mu_0$ = permeability of free space).

Vedclass Test Series

Exam Paper Generator

Online Exam Module