A current loop in a magnetic field: | vedclass

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

Question

(D) When a current loop is placed in a magnetic field,it experiences a torque given by $\vec{	au} = \vec{M} 	imes \vec{B}$,where $\vec{M}$ is the ma

Vedclass · Accepted Answer

can be in equilibrium in two orientations,one stable while the other is unstable.

Vedclass · Answer

(D) When a current loop is placed in a magnetic field,it experiences a torque given by $\vec{	au} = \vec{M} 	imes \vec{B}$,where $\vec{M}$ is the magnetic moment and $\vec{B}$ is the magnetic field.The magnitude of the torque is $	au = MB \sin 	heta$,where $	heta$ is the angle between $\vec{M}$ and $\vec{B}$.Equilibrium occurs when the torque is zero,which happens when $\sin 	heta = 0$,i.e.,$	heta = 0^{\circ}$ or $	heta = 180^{\circ}$.$1$. When $	heta = 0^{\circ}$,$\vec{M}$ and $\vec{B}$ are parallel. This is a state of minimum potential energy $(U = -\vec{M} \cdot \vec{B} = -MB)$,which corresponds to stable equilibrium.$2$. When $	heta = 180^{\circ}$,$\vec{M}$ and $\vec{B}$ are antiparallel. This is a state of maximum potential energy $(U = +MB)$,which corresponds to unstable equilibrium.Thus,the loop can be in equilibrium in two orientations,one stable and one unstable.

$A$ current loop in a magnetic field:

Similar Questions

$A$ uniform magnetic field $B$ of $0.3\, T$ is along the positive $Z-$ direction. $A$ rectangular loop $(abcd)$ of sides $10\, cm \times 5\, cm$ carries a current $I$ of $12\, A$. Out of the following different orientations,which one corresponds to stable equilibrium?

$A$ conducting ring of mass $2 \ kg$ and radius $0.5 \ m$ is placed on a smooth horizontal plane. The ring carries a current $i = 4 \ A$. $A$ horizontal magnetic field $B = 10 \ T$ is switched on at time $t = 0$ as shown in the figure. The initial angular acceleration of the ring will be:

Four wires each of length $2.0 \, m$ are bent into four loops $P$,$Q$,$R$ (labeled as $P$ in the image,but distinct),and $S$ and then suspended in a uniform magnetic field. The same current is passed through each loop. Which statement is correct?

$A$ uniform magnetic field of $0.3 \text{ T}$ is established along the $+z$-direction. $A$ rectangular loop of sides $10 \text{ cm}$ and $5 \text{ cm}$ carries a current of $12 \text{ A}$ and is placed in the $xy$-plane as shown in the figure. The torque acting on the loop is $....... \text{ Nm}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module