A square loop ABCD carries a current i and is | vedclass

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

Question

(B) The magnetic field $B$ at a distance $r$ from a long straight wire is given by $B = \frac{\mu_0 I}{2\pi r}$.The force on a current-carrying segmen

Vedclass · Accepted Answer

$\frac{2\mu_0 Ii}{3\pi}$

Vedclass · Answer

(B) The magnetic field $B$ at a distance $r$ from a long straight wire is given by $B = \frac{\mu_0 I}{2\pi r}$.The force on a current-carrying segment of length $L$ in a magnetic field is $F = BiL$.For the square loop,the sides parallel to the wire $XY$ experience forces,while the sides perpendicular to the wire experience equal and opposite forces that cancel out.$1$. Force on the side closer to the wire (distance $r_1 = L/2$): $F_1 = \left( \frac{\mu_0 I}{2\pi (L/2)} \right) i L = \frac{\mu_0 Ii}{\pi}$. This force is attractive (towards the wire).$2$. Force on the side farther from the wire (distance $r_2 = L/2 + L = 3L/2$): $F_2 = \left( \frac{\mu_0 I}{2\pi (3L/2)} \right) i L = \frac{\mu_0 Ii}{3\pi}$. This force is repulsive (away from the wire).The net force $F_{net} = F_1 - F_2 = \frac{\mu_0 Ii}{\pi} - \frac{\mu_0 Ii}{3\pi} = \frac{2\mu_0 Ii}{3\pi}$.

$A$ square loop $ABCD$ carries a current $i$ and is placed near a long straight wire $XY$ carrying a current $I$ as shown in the figure. What is the net force on the loop?

Similar Questions

An infinitely long current-carrying wire and a small current-carrying loop are in the plane of the paper as shown. The radius of the loop is $a$ and the distance of its centre from the wire is $d$ $(d >> a)$. If the loop applies a force $F$ on the wire,then:

$A$ 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 conductor and the side $AB$ is $L/2$. The net force on the loop will be:

The magnetic force on a current-carrying wire in an external uniform magnetic field depends on:

Two long and parallel straight wires $A$ and $B$ carrying currents of $8.0 \, A$ and $5.0 \, A$ in the same direction are separated by a distance of $4.0 \, cm$. Estimate the force on a $10 \, cm$ section of wire $A$.

What is the magnitude of magnetic force per unit length (in $N \;m^{-1}$) on a wire carrying a current of $8 \;A$ and making an angle of $30^{\circ}$ with the direction of a uniform magnetic field of $0.15 \;T$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module