A rigid square loop of side $a$ and carrying current $I_2$ is laying on a horizontal surface near a long current $I_1$ wire in the same plane as shown in figure. The net force on the loop due to the wire will be
JEE MAIN 2019, Diffcult
Download our app for free and get started
${{\text{F}}_3}{\text{& }}{{\text{F}}_4}\,{\text{cancel}}\,{\text{each}}\,{\text{other}}{\text{. }}$
${\text{Force on PQ will be }}{{\text{F}}_1} = {2_B}{\text{Ia}}$
${\text{ = }}{{\text{I}}_2}\frac{{{\mu _0}{I_1}}}{{2\pi {\text{a}}}}{\text{a}}$
$ = \frac{{{\mu _0}I}}{{2\pi {\text{a}}}}{\text{a}}$
$ = \frac{{{\mu _0}{I_1}{I_2}}}{{2\pi }}$
Force on $RS$ will be $F_{2}=I_{2} B_{2} a$
${=\mathrm{I}_{2} \frac{\mu_{0} \mathrm{I}_{1}}{2 \pi 2 \mathrm{a}} \mathrm{a}}$
${=\frac{\mu_{0} I_{1} I_{2}}{4 \pi}}$
Net force $=\mathrm{F}_{1}-\mathrm{F}_{2}=\frac{\mu_{0} I_1 \mathrm{I}_{2}}{4 \pi}$ repulsion
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A galvanometer coil of resistance $50 \,\Omega$, show full deflection of $100\,\mu A$. The shunt resistance to be added to the galvanometer, to work as an ammeter of range $10\, mA$ isView Solution
- 2The magnetic field at the origin due to a current element $i\,\overrightarrow {dl} $ placed at position $\vec r$ isView Solution
$(i)\,\,\left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{d\vec l\, \times \,\vec r}}{{{r^3}}}} \right)$
$(ii)\,\, - \left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{d\vec l\, \times \,\vec r}}{{{r^3}}}} \right)$
$(iii)\,\left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{\,\vec r \times d\vec l}}{{{r^3}}}} \right)$
$(iv)\, - \left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{\,\vec r \times d\vec l}}{{{r^3}}}} \right)$
- 3A uniformly charged dielectric ring rotating with constant angular velocity $'\omega '$ about its geometrical axis then it producesView Solution
- 4View SolutionTwo parallel beams of electrons moving in the same direction produce a mutual force
- 5View SolutionChoose the correct statement
- 6A rectangular region of dimensions ( $\omega \times l(\omega) \ll l$ ) has a constant magnetic field into the plane of the paper as shown in the figure below. On one side, the region is bounded by a screen. On the other side, positive ions of mass $m$ and charge $q$ are accelerated from rest and towards the screen by a parallel plate capacitor at constant potential difference $V < 0$ and come out through a small hole in the upper plate. Which one of the following statements is correct regarding the charge on the ions that hit the screen?View Solution
- 7A square shaped wire loop of mass $m$, resistance $R$ and side $a$ moving speed $v_{0}$, parallel to the $X$-axis, enters a region of uniform magnetic field $B$, which is perpendicular to the plane of the loop. The speed of the loop changes with distance $x(x < a)$ in the field, asView Solution
- 8View SolutionTwo wires of same length are shaped into a square and a circle. If they carry same current, ratio of the magnetic moment is
- 9Two long straight wires are placed along $x$-axis and $y$-axis. They carry current $I_1$ and $I_2$ respectively. The equation of locus of zero magnetic induction in the magnetic field produced by them isView Solution
- 10In the figure shown a current $I_1$ is established in the long straight wire $AB$.Another wire $CD$ carrying current $I_2$ is placed in the plane of the paper. The line joining the ends of this wire is perpendicular to the wire $AB$. The force on the wire $CD$ is:View Solution
