A magnetised wire of moment $M$ is bent into an arc of a circle subtending an angle of $60^o$ at the centre; then the new magnetic moment is
Diffcult
Download our app for free and get started
From figure
$\sin \frac{\theta}{2}=\frac{x}{r}$
$\Rightarrow x=\operatorname{rsin} \frac{\theta}{2}$
Hence new magnetic moment $M$
$=\mathrm{m}(2 \mathrm{x})=\mathrm{m} 2 \mathrm{rsin} \frac{\theta}{2}$
$=\mathrm{m} \cdot \frac{2 l}{\theta} \sin \frac{\theta}{2}=\frac{2 \mathrm{ml} \sin \theta / 2}{\theta}=\frac{2 \mathrm{M} \sin (\pi / 6)}{\pi / 3}=\frac{3 \mathrm{M}}{\pi}$
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
- 1Current through $ABC$ and $A'B'C'$ is $I$. What is the magentic field at $P$ ? $BP = PB' = r$ (Here $C'B'PBC$ are collinear)View Solution
- 2Two long parallel wires carrying equal current separated by $1\,m$, exert a force of $2 \times {10^{ - 7}}\,N/m$ on one another. The current flowing through them isView Solution
- 3Two infinitely long wires each carrying current $I$ along the same direction are made into the geometry as shown in the figure below. The magnetic field at the point $P$ isView Solution
- 4Three long, straight parallel wires carrying current, are arranged as shown in figure. The force experienced by a $25\, cm$ length of wire $C$ isView Solution
- 5Circular region of radius $R$ has uniform magnetic field $B = {B_0} + {B_0}t\left( { - \hat k} \right).\,At\,\,t\, = 0\,$ acceleration of charged particleView Solution
- 6The magnetic field at the origin due to a current element $i\,\overrightarrow {dl} $ placed at position $\vec r$ isView Solution
$(i)\,\,\left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{d\vec l\, \times \,\vec r}}{{{r^3}}}} \right)$
$(ii)\,\, - \left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{d\vec l\, \times \,\vec r}}{{{r^3}}}} \right)$
$(iii)\,\left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{\,\vec r \times d\vec l}}{{{r^3}}}} \right)$
$(iv)\, - \left( {\frac{{{\mu _0}i}}{{4\pi }}} \right)\left( {\frac{{\,\vec r \times d\vec l}}{{{r^3}}}} \right)$
- 7View SolutionWhich of the following statement is wrong
- 8A steel wire has a magnetic moment $M.$ What will be its magnetic moment if it is bent into a semi-circular arc ?View Solution
- 9A solenoid is oriented end-on so that its opening is perpendicular to the circuit containing the two light bulbs as drawn in figure $C_1.$ For figure $C_2$ and $C_3,$ a shorting wire of negligible resistance is added as shown. Assume that the magnetic field from the solenoid, shown coming out of the plane of the page, decreases uniformly with time at the same rate for each circuit. Rank the circuits for the brightness of the bulb labeled $R_1$ from brightest to dimmest.View Solution
- 10A long solenoid is fabricated to closely winding wire of radius $0.5\,mm$ over a cylindrical frame so that the successive turns nearly touch each other, the magnetic field at the centre of solenoid if it carries a current of $5\,A$View Solution