A magnetic dipole is under the influence of t | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) In stable equilibrium, the net torque acting on the magnetic dipole is zero. The torque due to field $B_1$ must balance the torque due to field $B

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(B) In stable equilibrium, the net torque acting on the magnetic dipole is zero. The torque due to field $B_1$ must balance the torque due to field $B_2$.Let $M$ be the magnetic moment of the dipole. The torque due to $B_1$ is $	au_1 = M B_1 \sin(90^{\circ} - 	heta) = M B_1 \cos 	heta$.The torque due to $B_2$ is $	au_2 = M B_2 \sin 	heta$.For equilibrium, $	au_1 = 	au_2$, so $M B_1 \cos 	heta = M B_2 \sin 	heta$.Rearranging the terms, we get $	an 	heta = \frac{B_1}{B_2}$.Substituting the given values:$	an 	heta = \frac{0.5 	imes 10^{-3}}{0.866 	imes 10^{-3}} = \frac{0.5}{0.866} \approx \frac{0.5}{0.5 \sqrt{3}} = \frac{1}{\sqrt{3}}$.Since $	an 	heta = \frac{1}{\sqrt{3}}$, we have $	heta = 30^{\circ}$.

$A$ magnetic dipole is under the influence of two orthogonal magnetic fields, $B_1 = 0.5 \times 10^{-3} \ T$ and $B_2 = 0.866 \times 10^{-3} \ T$. If the dipole comes to stable equilibrium at an angle $\theta$ with respect to the $B_2$ field, then the value of $\theta$ is (in $^{\circ}$)

Similar Questions

The work done in turning a magnet of magnetic moment $M$ by an angle of $90^{\circ}$ from the magnetic meridian is $n$ times the corresponding work done to turn it through an angle of $60^{\circ}$. The value of $n$ is:

$A$ short bar magnet placed with its axis at $30^{\circ}$ to a uniform external magnetic field of $0.5 \ T$ experiences a torque of magnitude equal to $4.5 \times 10^{-2} \ J$. The magnitude of the magnetic moment is . . . . . . .

$A$ small magnetized needle $P$ is placed at point $O$,and the arrow shows the direction of its magnetic moment. The other arrows show different positions (and orientations) of another identical magnet $Q$. In which configuration is the system $NOT$ in equilibrium?

Points $A$ and $B$ are situated perpendicular to the axis of a small bar magnet at large distances $x$ and $3x$ from its centre on opposite sides. The ratio of the magnetic fields at $A$ and $B$ will be approximately equal to

Write an expression for the magnitude of the magnetic field at a point lying on the equatorial line of a bar magnet.

Vedclass Test Series

Exam Paper Generator

Online Exam Module