A coil in the shape of an equilateral triangle of side $2 \mathrm{~cm}$ is suspended from a vertex such that…
A coil in the shape of an equilateral triangle of side $2 \mathrm{~cm}$ is suspended from a vertex such that it hangs in a vertical plane between the poles of a permanent magnet producing a horizontal magnetic field of $100 \times 10^{-3} \mathrm{~T}$. The magnetic field is parallel to the plane of the coil. For the moment of couple acting on the coil to be $2 \sqrt{3} \times 10^{-5} \mathrm{Nm}$, the current to be passed through the coil is
0.5 A
1 A
2 A
4 A
Solution
Given, magnetic field, $B=100 \times 10^{-3} \mathrm{~T}$
Torque, $\tau=2 \sqrt{3} \times 10^{-5} \mathrm{Nm}$
Now, torque $\tau=M B=I A B$
where, $M=$ magnetic dipole moment,
$B=$ magnetic field
$I=$ current to be passed through the coil.
Putting the given values in above expression, $2 \sqrt{3} \times 10^{-5}=I \cdot \sqrt{3} \times 10^{-4} \times 100 \times 10^{-3}$ or $I=2 \mathrm{~A}$