Question

Find an epression for torque on rectanglular coil in a uniform magnetic field

Answer 1

Answer:

Consider a rectangular coil PQRS suspended in a uniform magnetic field

B-, with its axis perpendicular to the field.

Figure (a) A rectangular loop PQRS in a uniform magnetic field B (b) Top view of the loop, magnetic dipole moment m+ is shown.

Let 1 = current flowing through the coil

PORS A=ab = area of the coil

a,b = sides of the coil PQRS

e = angle between the direction of B and normal to the plane of the coil.

According to Fleming's left hand rule, the magnetic forces on sides PS and QR are equal, opposite and collinear (along the axis of the loop), so their resultant is zero

inward force equal to IbB while the side RS experiences an equal normal outward force. These two forces for a couple which exerts a torque given by

T= Force x perpendicular distance =IBAsine

=lbBxasine

If the rectangular loop has N turns, the torque increases N times i.e.,

T= NIBAsine But NIA=m, the magnetic moment of the loop, so

TEMBsine

In vector notation, the torque t is given by

To=m+xB

The direction of the torque t is such that

The direction of the torque t is such that it rotates the loop clockwise about the axis of suspension.