A square loop ABCD of side length L carrying | vedclass

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

Question

(B) The force on a current-carrying wire near a long straight conductor is given by $F = \frac{{\mu _0}IiL}{2\pi r}$.For the side of the loop nearest

Vedclass · Accepted Answer

$\frac{{2{\mu _0}Ii}}{{3\pi }}$

Vedclass · Answer

(B) The force on a current-carrying wire near a long straight conductor is given by $F = \frac{{\mu _0}IiL}{2\pi r}$.For the side of the loop nearest to the wire (distance $r_1 = L/2$),the current flows in the same direction as the wire $XY$. The force $F_1$ is attractive:$F_1 = \frac{{\mu _0}IiL}{2\pi (L/2)} = \frac{{\mu _0}Ii}{\pi}$.For the side of the loop farthest from the wire (distance $r_2 = L/2 + L = 3L/2$),the current flows in the opposite direction to the wire $XY$. The force $F_2$ is repulsive:$F_2 = \frac{{\mu _0}IiL}{2\pi (3L/2)} = \frac{{\mu _0}Ii}{3\pi}$.The forces on the top and bottom sides of the loop are equal and opposite,so they cancel out.The net force is $F_{net} = F_1 - F_2 = \frac{{\mu _0}Ii}{\pi} - \frac{{\mu _0}Ii}{3\pi} = \frac{{\mu _0}Ii}{\pi} (1 - 1/3) = \frac{2{\mu _0}Ii}{3\pi}$.

$A$ square loop $ABCD$ of side length $L$ carrying a current $i$ is placed near and coplanar with a long straight conductor $XY$ carrying a current $I$. The distance between the wire $XY$ and the nearest side of the loop is $L/2$. The net force on the loop will be:

Similar Questions

$A$ triangular shaped wire carrying $10 A$ current is placed in a uniform magnetic field of $0.5 T$,as shown in the figure. The magnetic force on segment $CD$ is $.... N$ (Given $BC = CD = BD = 5 cm$).

Through two parallel wires $A$ and $B$,$10 \, A$ and $2 \, A$ of currents are passed respectively in opposite directions. If the wire $A$ is infinitely long and the length of the wire $B$ is $2 \, m$,the force on the conductor $B$,which is situated at a $10 \, cm$ distance from $A$,will be:

Wires $1$ and $2$ carrying currents $i_1$ and $i_2$ respectively are inclined at an angle $\theta$ to each other. What is the force on a small element $dl$ of wire $2$ at a distance of $r$ from wire $1$ (as shown in figure) due to the magnetic field of wire $1$?

$A$ straight wire of length $50 \text{ cm}$ carrying a current of $2.5 \text{ A}$ is suspended in mid-air by a uniform magnetic field of $0.5 \text{ T}$. Calculate the mass of the wire. (Take $g = 10 \text{ m s}^{-2}$) (in $\text{ g}$)

$A$ conductor of length $l$ and mass $m$ is placed along the east-west line on a table. Suddenly,a certain amount of charge is passed through it and it is found to jump to a height $h$. The earth's magnetic induction is $B$. The charge passed through the conductor is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module