Current round Cone!

Relevant wiki: Magnetic Moment

Two torques are acting on the cone, one is due to the gravitational force and second is due to the magnetic field. The torque of gravity is acting anticlockwise about the point P and trying to keep the cone in its position while the torque of magnetic field is acting in clockwise direction and trying to topple it.

To calculate the torque due to magnetic field, the cone can be imagined as made up of large many small current carrying rings. Each ring a can treated as a magnetic dipole and the net magnetic dipole moment of the cone can be calculated by adding the magnetic moments ( $i \times A$ ) of these individual rings.
Once magnetic moment of the cone is calculated, torque can be found out as $\vec{\tau}=\vec{M} \times \vec{B}$

Now, imagine a ring of width dx at a depth x from the apex as shown below.

The current flowing in this ring can be calculated by unitary method.
$\text{di} = \dfrac{\text{total current}}{\text{curved surface area of cone}} \times \text{area of the ring}$

The area of the ring is $\pi r dl$
$\text{di}=\dfrac{i}{\pi R L} \times 2\pi r dl$

Here, L is the slant height.
$dl \cos\theta = dx$

Also, $\tan\theta = \dfrac{x}{r} = \dfrac{h}{R}$

The magnetic dipole moment (dM) of the elemental ring assumed is $dM = di \times \text{Area of the loop}$
Therefore,
$M =\displaystyle \int_0^h {\left( {\dfrac{i}{{\pi RL}}2\pi \dfrac{{Rx}}{h}\dfrac{{dx}}{{\cos \theta }}} \right)} \times \pi {\left( {\dfrac{{Rx}}{h}} \right)^2}$

$M = \dfrac{{i\pi {R^2}}}{2}$
The direction of the magnetic dipole moment can be calculated by the right hand rule as vertically upwards.

Torque due to magnetic field on the cone will be given by
$\tau = M B \sin\theta$
The direction of this torque will be into the plane and will try to rotate the cone clockwise.

To prevent toppling, the torque of magnetic field should not exceed the torque of gravity about the point P,
Therefore,
$\dfrac{{i\pi {R^2}}}{2}B_0\sin {90^ \circ } = mgR$
$i = \dfrac{{2mg}}{{\pi R{B_0}}}$
Hence, the answer is 2.