Name: Magnetic Dipole and Dipole Moment
Uploaded: 2019-07-19
Duration: 4 min 53 s
Description: A magnetic dipole is an arrangement of two unlike magnetic poles of equal pole strength separated by a minimal distance. Let's learn more about them.

Question

Obtain an expression for torque acting on a current carrying loop in magnetic field in terms of the angle which normal to the plane of loop (coil) makes with magnetic field and in terms of angle which plane of the coil makes with magnetic field.

Accepted Answer

Its construction is shown in fig which consists of a rectangular, or circular, coil made by winding many turns of fine insulated copper wire on a light, non-magnetic, metallic frame. The coil is suspended by a thin phosphor-bronze strip from a torsion-head which is connected to a terminal screw $T_{1}$ . To the lower portion of the strip is attached a small light mirror which rotates along with the strip and its deflection can be measured by a lamp and scale arrangement. The lower end of the coil is connected to a fine, loosely-wound, spring which is connected to another terminal screw $T_{2}$ .

The coil hangs in the space between the pole-pieces of a powerful permanent horse-shoe magnet $NS$ . A soft-iron cylindrical piece is fixed within the coil, which is called the ‘core’. The core does not touch the coil anywhere. The whole arrangement is enclosed in a nonmagnetic box to protect it from air draughts.

Theory and working : When the terminal screws $T_{1}$ and $T_{2}$ of the galvanometer are connected to a current-carrying circuit, a current flows in the coil of the galvanometer. Since the coil is suspended in a magnetic field, a deflecting torque acts upon it. Due to this torque, the coil starts rotating from its position. Suppose, at any instant, the normal to the plane of the coil makes an angle $θ$ with the direction of the magnetic field. If $N$ be the number of turns in the coil, $A$ the area of the plane of the coil and $B$ the magnitude of the magnetic field, then the instantaneous deflecting torque is given by $τ = NIABsin θ$ ,

Suppose, in the equilibrium position, the angle of twist in the suspension strip is $ϕ$ radian. The deflecting torque acting on the coil will be $NIAB sin θ$ . If the restoring torque for an $C ϕ$ then in the equilibrium position of the coil, we have

$NIABsin θ = C ϕ$ $\Rightarrow I = \frac{C ϕ}{NABsin θ}$ $⇒I \propto \frac{ϕ}{\sin θ}$

In the condition of radial field $θ = 90 °$ . Hence, the deflecting torque on the coil suspended in radial magnetic field is always $N I A B$ . Then, in equilibrium position, we have $NIAB = C ϕ$ $⇒I = \frac{C}{NAB} ϕ$ $⇒I = K ϕ$

where $K = \frac{C}{N A B}$ is a constant which is called the ‘reduction factor' of the galvanometer. Thus, $I \propto ϕ$ ,

i.e. the current flowing in the coil is directly proportional to the deflection ot the coil.

Obtain an expression for torque acting on a current carrying loop in magnetic field in terms of the angle which normal to the plane of loop (coil) makes with magnetic field and in terms of angle which plane of the coil makes with magnetic field.

Important Questions on Torque on a Current-Loop : Moving-Coil Galvanometer

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