A square loop is carrying a steady current $I$ and the magnitude of its magnetic dipole moment is $m$. If this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be
JEE MAIN 2019, Medium
Download our app for free and get started
$m = I{l^2}$ $2\pi r = 4l$
${{{\text{m}}^\prime } = \frac{{I4{\ell ^2}}}{\pi }}$ ${{\text{r}} = \frac{{2\ell }}{\pi }}$
${{{\text{m}}^\prime } = \frac{{I4{\ell ^2}}}{\pi }}$ ${\pi {r^2} = \frac{{\pi 4{\ell ^2}}}{{{\pi ^2}}} = \frac{{4{\ell ^2}}}{\pi }}$
${{{\text{m}}^\prime } = \frac{4}{\pi }\,{\text{m}}}$
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
- 1An electron gun is placed inside a long solenoid of radius $\mathrm{R}$ on its axis. The solenoid has $\mathrm{n}$ turns/length and carries a current $I$. The electron gun shoots an electron along the radius of the solenoid with speed $v$. If the electron does not hit the surface of the solenoid, maximum possible value of ${v}$ is (all symbols have their standard meaning)View Solution
- 2Two ions of masses $4 \,{amu}$ and $16\, amu$ have charges $+2 {e}$ and $+3 {e}$ respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :View Solution
- 3View SolutionA uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron
- 4A conductor in the form of a right angle $ABC$ with $AB = 3\, cm$ and $BC = 4\, cm$ carries a current of $10\, A$. There is a uniform magnetic field of $5\, T$ perpendicular to the plane of the conductor. The force on the conductor will be......$N$View Solution
- 5A moving coil galvanometer, having a resistance $G$, produces full scale deflection when a current $I_g$ flows through it. This galvanometer can be converted into $(i)$ an ammeter of range $0$ to $I_0 (I_0 > I_g)$ by connecting a shunt resistance $R_A$ to it and $(ii)$ into a voltmeter of range $0$ to $V(V = GI_0)$ by connecting a series resistance $R_V$ to it. Then,View Solution
- 6A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbitals in a plane due to magnetic field perpendicular to the plane. Let $r_p, r_e$ and $r_{He}$ be their respective radii, thenView Solution
- 7A proton of mass $1.67 \times {10^{ - 27}}\,kg$ and charge $1.6 \times {10^{ - 19}}\,C$ is projected with a speed of $2 \times {10^6}\,m/s$ at an angle of $60^\circ $ to the $X - $ axis. If a uniform magnetic field of $0.104$ $Tesla$ is applied along $Y - $ axis, the path of proton isView Solution
- 8Two thick wires and two thin wires, all of the same materials and same length form a square in the three different ways $P$, $Q$ and $R$ as shown in fig with current connection shown, the magnetic field at the centre of the square is zero in casesView Solution
- 9A proton is accelerating in a cyclotron where the applied magnetic field is $2 \,T$. If the potential gap is effectively $100 \,kV$ then how much revolutions the proton has to make between the "dees" to acquire a kinetic energy of $20 \,MeV$ ?View Solution
- 10Two particles $x$ and $y$ have equal charges and possessing equal kinetic energy enter in a uniform magnetic field and describe circular path of radius of curvature $r_1$ and $r_2$ respectively. The ratio of their masses isView Solution