A square loop ABCD of side L carrying a curre | vedclass

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

Question

(C) The magnetic field $B$ at a distance $r$ from a long straight wire carrying current $I_2$ is given by $B = \frac{\mu_0 I_2}{2\pi r}$.For the squar

Vedclass · Accepted Answer

$\frac{9\mu_0 I_1 I_2}{8\pi}$

Vedclass · Answer

(C) The magnetic field $B$ at a distance $r$ from a long straight wire carrying current $I_2$ is given by $B = \frac{\mu_0 I_2}{2\pi r}$.For the square loop, the forces on the top segment $BC$ and bottom segment $AD$ are equal and opposite, so they cancel each other out.The force on the segment $AB$ (at distance $r_1 = L/3$) is $F_{AB} = \frac{\mu_0 I_1 I_2 L}{2\pi (L/3)} = \frac{3\mu_0 I_1 I_2}{2\pi}$ (attractive, towards the wire).The force on the segment $CD$ (at distance $r_2 = L/3 + L = 4L/3$) is $F_{CD} = \frac{\mu_0 I_1 I_2 L}{2\pi (4L/3)} = \frac{3\mu_0 I_1 I_2}{8\pi}$ (repulsive, away from the wire).The net force $F_{net} = F_{AB} - F_{CD} = \frac{3\mu_0 I_1 I_2}{2\pi} - \frac{3\mu_0 I_1 I_2}{8\pi} = \frac{12\mu_0 I_1 I_2 - 3\mu_0 I_1 I_2}{8\pi} = \frac{9\mu_0 I_1 I_2}{8\pi}$.

$A$ square loop $ABCD$ of side $L$ carrying a current $I_1$ is placed at a distance $(L/3)$ from a straight conductor $XY$ carrying current $I_2$. The loop and the conductor are coplanar. The net force on the loop will be ($\mu_0$ = magnetic permeability).

Similar Questions

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 $0.15 \;T$?

When current passing through two parallel wires flows in the same direction,the force between them is $......$,while when current passes in opposite directions through the same wires,the force between them is $......$ (attraction,repulsion).

Two wires $2 \text{ mm}$ apart supply current to a $100 \text{ V}$,$1 \text{ kW}$ heater. The force per metre between the wires is (Given $\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module