A thin circular wire carrying a current $I$ has a magnetic moment $M$. The shape of the wire is changed to a square and it carries the same current. It will have a magnetic moment
Medium
Download our app for free and get started
(d) Initially for circular coil $L = 2\pi r$ and $M = i \times \pi {r^2}$
$ = i \times \pi {\left( {\frac{L}{{2\pi }}} \right)^2} = \frac{{i{L^2}}}{{4\pi }}$ ..... $(i)$
Finally for square coil $M' = i \times {\left( {\frac{L}{4}} \right)^2} = \frac{{i{L^2}}}{{16}}$ ..... $(ii)$
Solving equation $(i)$ and $(ii)$ $M' = \frac{{\pi M}}{4}$
$ = i \times \pi {\left( {\frac{L}{{2\pi }}} \right)^2} = \frac{{i{L^2}}}{{4\pi }}$ ..... $(i)$
Finally for square coil $M' = i \times {\left( {\frac{L}{4}} \right)^2} = \frac{{i{L^2}}}{{16}}$ ..... $(ii)$
Solving equation $(i)$ and $(ii)$ $M' = \frac{{\pi M}}{4}$
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 wire of length $314\,cm$ carrying current of $14\,A$ is bent to form a circle. The magnetic moment of the coil is $........A- m ^{2}$. [Given $\left.\pi=3.14\right]$View Solution
- 2$AB$ and $CD$ are smooth parallel rails, separated by a distance $l$, and inclined to the horizontal at an angle $\theta$ . $A$ uniform magnetic field of magnitude $B$, directed vertically upwards, exists in the region. $EF$ is a conductor of mass $m$, carrying a current $i$. For $EF$ to be in equilibrium,View Solution
- 3Due to the flow of current in a circular loop of radius $R$, the magnetic field produced at the centre of the loop is $B$. The manetic moment of the loop isView Solution
- 4The coil of a galvanometer consists of $100$ $turns$ and effective area of $1\, square-cm$. The restoring couple is ${10^{ - 8}}\,N - m/radian$. The magnetic field between the pole pieces is $5\, T$. The current sensitivity of this galvanometer will beView Solution
- 5A long solenoid is producing magnetic field on its axis is $B$. If it is cuts into four equal parts and for same current, half number of turns wound on any on piece than value of magnetic field on it axis becomesView Solution
- 6The magnetic field at the centre of a circular coil of radius $I$, due to current I flowing through it, is $B$. The magnetic field at a point along the axis at a distance $\frac{r}{2}$ from the centre isView Solution
- 7A particle having a mass of $10^{- 2} \,kg$ carries a charge of $5 \times 10^{-8}\, C.$ The particle is given an initial horizontal velocity of $10^5\, m/s $ in the presence of electric field $E$ and magnetic field $B.$ To keep the particle moving in a horizontal direction, it is necessary thatView Solution
$(1)$ $\vec B$ should be perpendicular to the direction of velocity and $\vec E$ should be along the direction of velocity$(2)$ Both $\vec B$ and $\vec E$ should be along the direction of velocity$(3)$ Both $\vec B$ and $\vec E$ are mutually perpendicular and perpendicular to the direction of velocity.$(4)$ $\vec B$ should be along the direction of velocity and $\vec E$ should be perpendicular to the direction of velocityWhich one of the following pairs of statements is possible? - 8In a toroid the number of turns per unit length is $1000$ and current through it is $\frac{1}{4 \pi}$ ampere. The magnetic field produced inside (in $weber / m ^2$ ) will beView Solution
- 9View SolutionA charged particle is released from rest in a region of uniform electric and magnetic fields which are parallel to each other. The particle will move on a
- 10A square loop $ABCD$ carrying a current $i,$ is placed near and coplanar with a long straight conductor $XY$ carrying a current $I,$ the net force on the loop will beView Solution
