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
A$M$
B$\frac{4}{{{\pi ^2}}}M$
C$\frac{4}{\pi }M$
D$\frac{\pi }{4}M$
Medium
Download our app for free and get started
D$\frac{\pi }{4}M$
d (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 $(ii)$ $M' = \frac{{\pi M}}{4}$
Download our app
and 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.*
An electron is revolving round a proton, producing a magnetic field of $16\, weber/m^2$ in a circular orbit of radius $1\,\mathop A\limits^o $. It’s angular velocity will be
Following figure shows the path of an electron that passes through two regions containing uniform magnetic fields of magnitudes $B_1$ and $B_2$. It's path in each region is a half circle, choose the correct option
When a resistance of $5\,\Omega$ is shunted with a moving coil galvanometer, it shows a full scale deflection for a current of $250\,mA$, however when $1050\,\Omega$ resistance is connected with it in series, it gives full scale deflection for $25$ volt. The resistance of galvanometer is $......\,\Omega$.
A symmetric star conducting wire loop is carrying a steady state current $\mathrm{I}$ as shown in figure. The distance between the diametrically opposite vertices of the star is $4 a$. The magnitude of the magnetic field at the center of the loop is
If the maximum value of accelerating potential provided by a ratio frequency oscillator is $12\, {kV}$. The number of revolution made by a proton in a cyclotron to achieve one sixth of the speed of light is ....... .